# Items tagged with numericnumeric Tagged Items Feed

### singularity at endpoint...

Yesterday at 5:23 PM
0 1

Hi

It seems a singularity has been occurred at left end point for n less than unit (say n=0.5, n>0)

Is there a way to fix it?

n.mw

June 22 2016
0 0

DEAR SIR,

### how to compUTE CPU time in RK45 dsolve command?...

June 22 2016
0 2

DEAR SIR

ANYONE CAN HELP TO COMPUTE TIME IN DSOLVE COMMAND?

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### How to solve this PDE system?...

June 19 2016
0 6

bbb2.mw

 (1)

 (2)

 (3)

 (4)

 (5)

if former equations are not solvable , please help me for another way, in which at first two equation solve..in this way in equation [J and B] assume that q[311]=e[311]=0 and dsolve perform to find Φ and  ψ

after by finding Φ and  ψ is use for detemine w and u0

bbb2_2.mw

### Newton iteration is not converging...

June 15 2016
0 1

Dear All,

I am going to solve the following systems of ODEs but get the error: Newton iteration is not converging.
Could you please share your idea with me. In the case of AA=-0.2,0,0.2,0.4,...; I could get the solution.

restart;
with(plots);
Pr := 2; Le := 2; nn := 2; Nb := .1; Nt := .1; QQ := .1; SS := .1; BB := .1; CC := .1; Ec := .1; MM := .2;AA:=-0.4;

Eq1 := diff(f(eta), $(eta, 3))+f(eta).(diff(f(eta), $(eta, 2)))-2.*nn/(nn+1).((diff(f(eta), eta))^2)-MM.(diff(f(eta), eta)) = 0; Eq2 := 1/Pr.(diff(theta(eta), $(eta, 2)))+f(eta).(diff(theta(eta), eta))-4.*nn/(nn+1).(diff(f(eta), eta)).theta(eta)+Nb.(diff(theta(eta), eta)).(diff(h(eta), eta))+Nt.((diff(theta(eta), eta))^2)+Ec.((diff(f(eta), $(eta, 2)))^2)-QQ.theta(eta) = 0;
Eq3 := diff(h(eta), $(eta, 2))+Le.f(eta).(diff(h(eta), eta))+Nt/Nb.(diff(theta(eta), $(eta, 2))) = 0;

bcs := f(0) = SS, (D(f))(0) = 1+AA.((D@@2)(f))(0), theta(0) = 1+BB.(D(theta))(0), phi(0) = 1+CC.(D(phi))(0), (D(f))(etainf) = 0, theta(etainf) = 0, phi(etainf) = 0

Error, (in dsolve/numeric/ComputeSolution) Newton iteration is not converging

### Error in dsolve/numeric/bvp...

June 12 2016
1 7

I've been trying to numerically solve (and plot) this equation. Maple tells me that some matrix is singular - I have no idea, what I can do.

eq := diff(y(x), $(x, 3))-(diff(y(x), x))*(diff(y(x), x))+1 = 0; cond := (D(y))(0) = 0, (D(y))(1) = 1, ((D@@2)(y))(0) = 0 de := dsolve({cond, eq}, y(x), numeric); Error, (in dsolve/numeric/bvp) matrix is singular ### Error in optimal control problem... June 10 2016 1 1 I am unable to solve the attached optimal control problem,please any one who many help me in guideing .tnx restart: unprotect('gamma'); L:=b[1]*c(t)+b[2]*i(t)+w[1]*(u[1])^2/2+w[2]*(u[2])^2/2+w[3]*(u[3])^2/2; 1 2 1 2 1 2 b[1] c(t) + b[2] i(t) + - w[1] u[1] + - w[2] u[2] + - w[3] u[3] 2 2 2 H:=L+lambda[1](t)*((1-p*Psi)*tau+phi* v + delta *r-lambda*(1-u[3])*s-u[1]*varphi*s -mu*s ) +lambda[2](t)*(p*Psi*tau + u[1]*vartheta*s -gamma*lambda* (1-u[3])*v-(mu+phi)*v ) +lambda[3](t)*( (1-u[3])*rho*lambda* (s +gamma*v)+(1-q)* u[2]*eta*i -(mu +beta +chi)*c ) +lambda[4](t)* ((1-rho)*(1-u[3])*lambda*( s +gamma*v) +chi*c - u[2]*eta*i - (mu +alpha )*i) +lambda[5](t)*( beta*c + u[2]*q*eta*i -(mu +delta)*r); 1 2 1 2 1 2 b[1] c(t) + b[2] i(t) + - w[1] u[1] + - w[2] u[2] + - w[3] u[3] + lambda[1](t 2 2 2 ) ((1 - p Psi) tau + phi v + delta r - lambda (1 - u[3]) s - u[1] varphi s - mu s) + lambda[2](t) (p Psi tau + u[1] vartheta s - gamma lambda (1 - u[3]) v - (mu + phi) v) + lambda[3](t) ((1 - u[3]) rho lambda (s + gamma v) + (1 - q) u[2] eta i - (mu + beta + chi) c) + lambda[4](t ) ((1 - rho) (1 - u[3]) lambda (s + gamma v) + chi c - u[2] eta i - (mu + alpha) i) + lambda[5](t) (beta c + u[2] q eta i - (mu + delta) r) du1:=diff(H,u[1]); w[1] u[1] - lambda[1](t) varphi s + lambda[2](t) vartheta s du2:=diff(H,u[2]);du3:=diff(H,u[3]); w[2] u[2] + lambda[3](t) (1 - q) eta i - lambda[4](t) eta i + lambda[5](t) q eta i w[3] u[3] + lambda[1](t) lambda s + lambda[2](t) gamma lambda v - lambda[3](t) rho lambda (s + gamma v) - lambda[4](t) (1 - rho) lambda (s + gamma v) ddu1 := -A[1] u[1] + psi[1](t) beta x[1] x[3] - psi[2](t) beta x[1] x[3] ddu2 := -A[2] u[2] - psi[3](t) k x[2] sol_u1 := solve(du1, u[1]); s(t) (lambda[1](t) varphi - lambda[2](t) vartheta) -------------------------------------------------- w[1] sol_u2 := solve(du2, u[2]);sol_u3 := solve(du3, u[3]); eta i (-lambda[3](t) + lambda[3](t) q + lambda[4](t) - lambda[5](t) q) ---------------------------------------------------------------------- w[2] 1 ---- (lambda (-lambda[1](t) s - lambda[2](t) gamma v + lambda[3](t) rho s w[3] + lambda[3](t) rho gamma v + lambda[4](t) s + lambda[4](t) gamma v - lambda[4](t) rho s - lambda[4](t) rho gamma v)) Dx2:=subs(u[1]= s*(lambda[1](t)*varphi-lambda[2](t)*vartheta)/w[1] ,u[2]= eta*i*(-lambda[3](t)+lambda[3](t)*q+lambda[4](t)-lambda[5](t)*q)/w[2], u[3]=-lambda*(lambda[1](t)*s+lambda[2](t)*gamma*v-lambda[3](t)*rho*s-lambda[3](t)*rho*gamma*v-lambda[4](t)*s-lambda[4](t)*gamma*v+lambda[4](t)*rho*s+lambda[4](t)*rho*gamma*v)/w[3] ,H ); 2 2 s (lambda[1](t) varphi - lambda[2](t) vartheta) b[1] c(t) + b[2] i(t) + ------------------------------------------------- 2 w[1] 2 2 2 eta i (-lambda[3](t) + lambda[3](t) q + lambda[4](t) - lambda[5](t) q) + ------------------------------------------------------------------------- + 2 w[2] 1 / 2 ------ \lambda (lambda[1](t) s + lambda[2](t) gamma v - lambda[3](t) rho s 2 w[3] - lambda[3](t) rho gamma v - lambda[4](t) s - lambda[4](t) gamma v / \ | + lambda[4](t) rho s + lambda[4](t) rho gamma v)^2/ + lambda[1](t) |(1 \ / 1 - p Psi) tau + phi v + delta r - lambda |1 + ---- (lambda (lambda[1](t) s \ w[3] + lambda[2](t) gamma v - lambda[3](t) rho s - lambda[3](t) rho gamma v - lambda[4](t) s - lambda[4](t) gamma v + lambda[4](t) rho s \ + lambda[4](t) rho gamma v))| s / 2 \ s (lambda[1](t) varphi - lambda[2](t) vartheta) varphi | - ------------------------------------------------------- - mu s| + w[1] / / | lambda[2](t) |p Psi tau \ 2 s (lambda[1](t) varphi - lambda[2](t) vartheta) vartheta / + --------------------------------------------------------- - gamma lambda |1 + w[1] \ 1 ---- (lambda (lambda[1](t) s + lambda[2](t) gamma v - lambda[3](t) rho s w[3] - lambda[3](t) rho gamma v - lambda[4](t) s - lambda[4](t) gamma v \ \ | + lambda[4](t) rho s + lambda[4](t) rho gamma v))| v - (mu + phi) v| + / / // 1 lambda[3](t) ||1 + ---- (lambda (lambda[1](t) s + lambda[2](t) gamma v \\ w[3] - lambda[3](t) rho s - lambda[3](t) rho gamma v - lambda[4](t) s \ - lambda[4](t) gamma v + lambda[4](t) rho s + lambda[4](t) rho gamma v))| / 1 / 2 2 rho lambda (s + gamma v) + ---- \(1 - q) eta i (-lambda[3](t) w[2] \ \ + lambda[3](t) q + lambda[4](t) - lambda[5](t) q)/ - (mu + beta + chi) c| + / / | / 1 lambda[4](t) |(1 - rho) |1 + ---- (lambda (lambda[1](t) s \ \ w[3] + lambda[2](t) gamma v - lambda[3](t) rho s - lambda[3](t) rho gamma v - lambda[4](t) s - lambda[4](t) gamma v + lambda[4](t) rho s \ + lambda[4](t) rho gamma v))| lambda (s + gamma v) + chi c / 2 2 eta i (-lambda[3](t) + lambda[3](t) q + lambda[4](t) - lambda[5](t) q) - ------------------------------------------------------------------------ w[2] \ / | | - (mu + alpha) i| + lambda[5](t) |beta c / \ + 2 2 eta i (-lambda[3](t) + lambda[3](t) q + lambda[4](t) - lambda[5](t) q) q -------------------------------------------------------------------------- w[2] \ | - (mu + delta) r| / ode1:=diff(lambda[1](t),t)=-diff(H,s);ode2:=diff(lambda[2](t),t)=-diff(H,v);ode3:=diff(psi[3](t),t)=-diff(H,c);ode4:=diff(lambda[4](t),t)=-diff(H,i);ode5:=diff(lambda[5](t),t)=-diff(H,r); d --- lambda[1](t) = -lambda[1](t) (-lambda (1 - u[3]) - u[1] varphi - mu) dt - lambda[2](t) u[1] vartheta - lambda[3](t) (1 - u[3]) rho lambda - lambda[4](t) (1 - rho) (1 - u[3]) lambda d --- lambda[2](t) = -lambda[1](t) phi dt - lambda[2](t) (-gamma lambda (1 - u[3]) - mu - phi) - lambda[3](t) (1 - u[3]) rho lambda gamma - lambda[4](t) (1 - rho) (1 - u[3]) lambda gamma d --- psi[3](t) = -lambda[3](t) (-mu - beta - chi) - lambda[4](t) chi dt - lambda[5](t) beta d --- lambda[4](t) = -lambda[3](t) (1 - q) u[2] eta dt - lambda[4](t) (-u[2] eta - mu - alpha) - lambda[5](t) u[2] q eta d --- lambda[5](t) = -lambda[1](t) delta - lambda[5](t) (-mu - delta) dt restart: #Digits:=10: unprotect('gamma'); lambda:=0.51: mu:=0.002: beta:=0.0115: delta:=0.003: alpha:=0.33: chi:=0.00274: k:=6.24: gamma:=0.4: rho:=0.338:;tau=1000:;Psi:=0.1:;p:=0.6:;phi:=0.001:;eta:=0.001124:q:=0.6:varphi:=0.9:;vatheta:=0.9: b[1]:=2:;b[2]:=3:;w[1]:=4:;w[2]:=5:;w[3]:=6: #u[1]:=s(t)*(lambda[1](t)*varphi-lambda[2](t)*vartheta)/w[1]: #u[2]:=eta*i*(-lambda[3](t)+lambda[3](t)*q+lambda[4](t)-lambda[5](t)*q)/w[2]:;u[3]:=lambda*(-lambda[1](t)*s-lambda[2](t)*gamma*v+lambda[3](t)*rho*s+lambda[3](t)*rho*gamma*v+lambda[4](t)*s+lambda[4](t)*gamma*v-lambda[4](t)*rho*s-lambda[4](t)*rho*gamma*v)/w[3]: ics := s(0)=8200, v(0)=2800,c(0)=1100,i(0)=1500,r(0)=200,lambda[1](20)=0,lambda[2](20)=0,lambda[3](20)=0,lambda[4](20)=0,lambda[5](20)=0: ode1:=diff(s(t),t)=(1-p*Psi)*tau+phi* v(t) + delta *r(t)-lambda*(1-u[3])*s(t)-u[1]*varphi*s(t) -mu*s(t), diff(v(t), t) =p*Psi*tau + u[1]*vartheta*s(t) -gamma*lambda* (1-u[3])*v(t)-(mu+phi)*v(t) , diff(c(t), t) =(1-u[3])*rho*lambda* (s(t) +gamma*v(t))+(1-q)* u[2]*eta*i(t) -(mu +beta +chi)*c(t), diff(i(t), t) =(1-rho)*(1-u[3])*lambda*( s(t) +gamma*v(t)) +chi*c(t) - u[2]*eta*i(t) - (mu +alpha )*i(t), diff(r(t), t) = beta*c(t) + u[2]*q*eta*i(t) -(mu +delta)*r(t), diff(lambda[1](t), t) = -lambda[1](t)*(-lambda*(1-u[3])-u[1]*varphi-mu)-lambda[2](t)*u[1]*vartheta-lambda[3](t)*(1-u[3])*rho*lambda-lambda[4](t)*(1-rho)*(1-u[3])*lambda,diff(lambda[2](t),t)=-lambda[1](t)*phi-lambda[2](t)*(-gamma*lambda*(1-u[3])-mu-phi)-lambda[3](t)*(1-u[3])*rho*lambda*gamma-lambda[4](t)*(1-rho)*(1-u[3])*lambda*gamma,diff(lambda[3](t),t)=-lambda[3](t)*(-mu-beta-chi)-lambda[4](t)*chi-lambda[5](t)*beta,diff(lambda[4](t),t)=-lambda[3](t)*(1-q)*u[2]*eta-lambda[4](t)*(-u[2]*eta-mu-alpha)-lambda[5](t)*u[2]*q*eta,diff(lambda[5](t),t)=-lambda[1](t)*delta-lambda[5](t)*(-mu-delta); d --- s(t) = (1 - p Psi) tau + phi v(t) + delta r(t) - lambda (1 - u[3]) s(t) dt d - u[1] varphi s(t) - mu s(t), --- v(t) = p Psi tau + u[1] vartheta s(t) dt d - gamma lambda (1 - u[3]) v(t) - (mu + phi) v(t), --- c(t) = (1 - u[3]) rho lambda dt (s(t) + gamma v(t)) + (1 - q) u[2] eta - (mu + beta + chi) c(t), 0 = (1 - rho) (1 - u[3]) lambda (s(t) + gamma v(t)) + chi c(t) - u[2] eta - mu d d - alpha, --- r(t) = beta c(t) + u[2] q eta - (mu + delta) r(t), --- dt dt lambda[1](t) = -lambda[1](t) (-lambda (1 - u[3]) - u[1] varphi - mu) - lambda[2](t) u[1] vartheta - lambda[3](t) (1 - u[3]) rho lambda d - lambda[4](t) (1 - rho) (1 - u[3]) lambda, --- lambda[2](t) = dt -lambda[1](t) phi - lambda[2](t) (-gamma lambda (1 - u[3]) - mu - phi) - lambda[3](t) (1 - u[3]) rho lambda gamma d - lambda[4](t) (1 - rho) (1 - u[3]) lambda gamma, --- lambda[3](t) = dt d -lambda[3](t) (-mu - beta - chi) - lambda[4](t) chi - lambda[5](t) beta, --- dt lambda[4](t) = -lambda[3](t) (1 - q) u[2] eta - lambda[4](t) (-u[2] eta - mu - alpha) - lambda[5](t) u[2] q eta, d --- lambda[5](t) = -lambda[1](t) delta - lambda[5](t) (-mu - delta) dt sol := dsolve({c(0) = 0, i(0) = 0, r(0) = .1, s(0) = 0, v(0) = 0, diff(c(t), t) = (1-u[3])*rho*lambda*(s(t)+gamma*v(t))+(1-q)*u[2]*eta*i(t)-(mu+beta+chi)*c(t), diff(i(t), t) = (1-rho)*(1-u[3])*lambda*(s(t)+gamma*v(t))+chi*c(t)-u[2]*eta*i(t)-(mu+alpha)*i(t), diff(r(t), t) = beta*c(t)+u[2]*q*eta*i(t)-(mu+delta)*r(t), diff(s(t), t) = (1-p*Psi)*tau+phi*v(t)+delta*r(t)-lambda*(1-u[3])*s(t)-u[1]*varphi*s(t)-mu*s(t), diff(v(t), t) = p*Psi*tau+u[1]*vartheta*s(t)-gamma*lambda*(1-u[3])*v(t)-(mu+phi)*v(t), diff(lambda[1](t), t) = -lambda[1](t)*(-lambda*(1-u[3])-u[1]*varphi-mu)-lambda[2](t)*u[1]*vartheta-lambda[3](t)*(1-u[3])*rho*lambda-lambda[4](t)*(1-rho)*(1-u[3])*lambda, diff(lambda[2](t), t) = -lambda[1](t)*phi-lambda[2](t)*(-gamma*lambda*(1-u[3])-mu-phi)-lambda[3](t)*(1-u[3])*rho*lambda*gamma-lambda[4](t)*(1-rho)*(1-u[3])*lambda*gamma, diff(lambda[3](t), t) = -lambda[3](t)*(-mu-beta-chi)-lambda[4](t)*chi-lambda[5](t)*beta, diff(lambda[4](t), t) = -lambda[3](t)*(1-q)*u[2]*eta-lambda[4](t)*(-u[2]*eta-mu-alpha)-lambda[5](t)*u[2]*q*eta, diff(lambda[5](t), t) = -lambda[1](t)*delta-lambda[5](t)*(-mu-delta), lambda[1](20) = 0, lambda[2](20) = 0, lambda[3](20) = 0, lambda[4](20) = 0, lambda[5](20) = 0}, type = numeric); Error, (in dsolve/numeric/process_input) invalid specification of initial conditions, got 1 = 0 sol:=dsolve([ode1,ics],numeric, method = bvp[midrich],maxmesh=500); Error, (in dsolve/numeric/process_input) system must be entered as a set/list of expressions/equations dsolve[':-interactive']({}); Error, := unexpected sol:=dsolve([ode1,ics],numeric, method = bvp[midrich],maxmesh=500); Error, (in dsolve/numeric/process_input) system must be entered as a set/list of expressions/equations eq1:=diff(s(t), t)=(1-p*Psi)*tau+phi* v(t) + delta *r(t)-lambda*(1-u[3])*s(t)-u[1]*varphi*s(t) -mu*s(t); eq2:diff(v(t), t) =p*Psi*tau + u[1]*vartheta*s(t) -gamma*lambda* (1-u[3])*v(t)-(mu+phi)*v(t); eq3:=diff(c(t), t) =(1-u[3])*rho*lambda* (s(t) +gamma*v(t))+(1-q)* u[2]*eta*i(t) -(mu +beta +chi)*c(t); eq4:=diff(i(t), t) =(1-rho)*(1-u[3])*lambda*( s(t) +gamma*v(t)) +chi*c(t) - u[2]*eta*i(t) - (mu +alpha )*i(t); eq5:=diff(r(t), t) = beta*c(t) + u[2]*q*eta*i(t) -(mu +delta)*r(t); d --- s(t) = (1 - p Psi) tau + phi v(t) + delta r(t) - lambda (1 - u[3]) s(t) dt - u[1] varphi s(t) - mu s(t) d --- v(t) = p Psi tau + u[1] vartheta s(t) - gamma lambda (1 - u[3]) v(t) dt - (mu + phi) v(t) d --- c(t) = (1 - u[3]) rho lambda (s(t) + gamma v(t)) + (1 - q) u[2] eta i(t) dt - (mu + beta + chi) c(t) d --- i(t) = (1 - rho) (1 - u[3]) lambda (s(t) + gamma v(t)) + chi c(t) dt - u[2] eta i(t) - (mu + alpha) i(t) d --- r(t) = beta c(t) + u[2] q eta i(t) - (mu + delta) r(t) dt eq6:=diff(Q(t),t)=b[1]*c(t)+b[2]*i(t)+w[1]*(u[1])^2/2+w[2]*(u[2])^2/2+w[3]*(u[3])^2/2; d 1 2 1 2 1 2 --- Q(t) = b[1] c(t) + b[2] i(t) + - w[1] u[1] + - w[2] u[2] + - w[3] u[3] dt 2 2 2 ics:=s(0)=8200, v(0)=2800,c(0)=1100,i(0)=1500,r(0)=200,Q(0)=6700; s(0) = 8200, v(0) = 2800, c(0) = 1100, i(0) = 1500, r(0) = 200, Q(0) = 6700 sol0:=dsolve({eq1,eq2,eq3,eq4,eq5,eq6,ics},type=numeric,stiff=true,'parameters'=[u[1],u[2],u[3]],abserr=1e-15,relerr=1e-12,maxfun=0,range=0..50): Error, (in dsolve/numeric/process_input) system must be entered as a set/list of expressions/equations with(plots): Q0:=6700; 6700 obj:=proc(u) global sol0,Q0; local ob1; try sol0('parameters'=[u[1],u[2],u[3]]): ob1:=subs(sol0(20.),Q(t)): catch : ob1:=0; end try; #ob1:=subs(sol0(20.),Q(t)); if ob1>Q0 then Q0:=ob1;print(Q0,u);end; ob1; end proc; proc(u) ... end; obj([1,1,1]); 0 obj([3,2.5],4); 0 u0:=Vector(3,[0.,0.,0.],datatype=float[8]); Vector[column](%id = 85973880) Q0:=0; Q0 := 0 with(Optimization); [ImportMPS, Interactive, LPSolve, LSSolve, Maximize, Minimize, NLPSolve, QPSolve] sol2:=NLPSolve(3,obj,initialpoint=u0,method=nonlinearsimplex,maximize,evaluationlimit=100): sol0('parameters'=[3.18125786060723, 2.36800986932868]); sol0(parameters = [3.18125786060723, 2.36800986932868]) for i from 1 to 3 do odeplot(sol0,[t,x[i](t)],0..20,thickness=3,axes=boxed);od; Error, (in plots/odeplot) input is not a valid dsolve/numeric solution ### Get result from pdsolve... June 09 2016 0 1 hello , how i can exract value from pdsolve ,i need to use dU(x,R)/dR thank you  >  >  (1)  >  (2)  >  (3)  >  (4)  >  (5)  >  (6)  >  >  >  > Download U(R)_numériqueg2.mw ### NLP optimization... June 09 2016 1 8 I have a nonlinear function Q(a,b,c,d,x,y) and I'd like to get the optimum (x*,y*) for different values of (a,b,c,d). The usual sintax: NLPSolve(Q(10, 1, 5, 2, x,y), x= 0 .. 50, y = 0 .. 50, initialpoint = {x = 2,y= .5}, assume = nonnegative) does not work when Q contains numerical integration, that is evalf (Int). I have no problem with the definite integral evalf(int). The problem is that most of the cases required numerical integration so I need the former expression. I'd appreciate very much if someone could help me. ### Problem with PDE solution ... June 08 2016 1 8 vz := 2*(-eta^2+1); D_im := .22; r0 := 1; pde := diff(vz*Y(eta, z), z)-D_im*((diff(eta*(diff(Y(eta, z), eta)), eta))/eta+diff(Y(eta, z), $(z, 2)))/r0 = 0;

pde := expand(%);

ibc := [Y(1, z) = 0, (D[1](Y))(0, z) = 0, Y(eta, 0) = 1, (D[2](Y))(eta, 0) = 0];

sol := pdsolve(pde, ibc, numeric, time = z, range = 0 .. 1);

pds := sol:-value(z = 0, output = listprocedure);

sol:-plot(z = 0.1e-3, numpoints = 50, color = blue, view = 0 .. 1)

So I was trying to solve this conservation equation for the radial coordinate eta and the z coordinate being treated as time. The flow is in z direction. Now unfortunately it is diverging. Not sure why though. What am I doing wrong?

### Problem with dsolve...

June 07 2016
1 3

Hello, My problem is as following:

I have tried 2 options for solving the problem below, trying to plot the behaviour of a system to a predetermined function.

First I tried to use dsolve as usual:

restart; with(plots); C := setcolors(); with(LinearAlgebra);
eq1 := Force = Mass*(diff(y(t), $(t, 2))); formula1 := 2.6*BodyWeight*abs(sin(4*Pi*t)); 2.6 BodyWeight |sin(4 Pi t)| BodyWeight := 80*9.81; plot(formula1, t = 0 .. 2); eq2 := formula1-SpringConstant*(diff(y(t), t)) = Mass*(diff(y(t), $(t, 2)));
/ d \ / d /
2040.480 |sin(4 Pi t)| - SpringConstant |--- y(t)| = Mass |--- |
\ dt / \ dt \

d \\
--- y(t)||
dt //
Mass := .200;
Springt := 200;
200
SpringConstant := Youngsmodulus*Surface/DeltaLength;
DeltaLength := 0.2e-1-y(t);
Surface := .15;
Youngsmodulus := 1600*10^6-20*t^2;
eq2;
/ 2 \ / d \
0.15 \-20 t + 1600000000/ |--- y(t)|
\ dt /
2040.480 |sin(4 Pi t)| - ------------------------------------- =
0.02 - y(t)

/ d / d \\
0.200 |--- |--- y(t)||
\ dt \ dt //

incs := y(0) = 0, (D(y))(0) = 0;
eq4 := dsolve({eq2, incs});
Warning: System is inconsistent

Second, I tried using a numerical solving, with maxfun.

restart; with(plots); C := setcolors(); with(LinearAlgebra);
eq1 := Force = Mass*(diff(y(t), $(t, 2))); formula1 := 2.6*BodyWeight*abs(sin(4*Pi*t)); 2.6 BodyWeight |sin(4 Pi t)| BodyWeight := 80*9.81; plot(formula1, t = 0 .. 2); eq2 := formula1-SpringConstant*(diff(y(t), t)) = Mass*(diff(y(t), $(t, 2)));
/ d \ / d /
2040.480 |sin(4 Pi t)| - SpringConstant |--- y(t)| = Mass |--- |
\ dt / \ dt \

d \\
--- y(t)||
dt //
Mass := .200;
Springt := 200;
200
SpringConstant := Youngsmodulus*Surface/DeltaLength;
DeltaLength := 0.2e-1-y(t);
Surface := .15;
Youngsmodulus := 1600*10^6-20*t^2;
eq2;
/ 2 \ / d \
0.15 \-20 t + 1600000000/ |--- y(t)|
\ dt /
2040.480 |sin(4 Pi t)| - ------------------------------------- =
0.02 - y(t)

/ d / d \\
0.200 |--- |--- y(t)||
\ dt \ dt //

incs := y(0) = 0, (D(y))(0) = 0;
eq4 := dsolve({eq2, incs}, y(t), type = numeric, output = listprocedure, maxfun = 10^7);
[
[t = proc(t) ... end;, y(t) = proc(t) ... end;,
[

d ]
--- y(t) = proc(t) ... end;]
dt ]

test := rhs(eq4[2]);
proc(t) ... end;

This one does plot, but no further than 0.2*10^-6. I have tried compiling the data, but this has not worked yet.

Does anyone know a way to work around such a problem. Is it possible to plot the equation using a for loop? If yes, how?

### A strange result from dsolve...

June 01 2016
2 2

Hello guys,

I was just playing around with differential equations, when I noticed that symbolic solution is  different from the numerical.What is the reason for this strange behavior?

ODE := (diff(y(x), x))*(ln(y(x))+x) = 1

sol := dsolve({ODE, y(1) = 1}, y(x))

a := plot(op(2, sol), x = .75 .. 2, color = "Red");
sol2 := dsolve([ODE, y(1) = 1], numeric, range = .75 .. 2);

with(plots);
b := odeplot(sol2, .75 .. 2, thickness = 4);
display({a, b});

Mariusz Iwaniuk

### Numerical solution of challenging ODE...

May 25 2016
1 7

Hello everybody.

I'm trying to obtain the numerical solution of a differential equation. Unfortunately, this prove to be quite challenging. I was able to obtain a rough solution using mathematica, but nothing more. The function is strictly increasing (for sure).

Any help is really REALLY appreciated, thanks!

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 (2)

 (3)

### How to get rid of error about unconvergence?...

May 18 2016
1 2

How can i over come convergence error, i am unable to apply approxsoln appropriately and continouation as well. regards

 (1)

 (2)

### Problem with solving ODE system...

May 13 2016
0 0

i have attcahed my ode with complex bvp

can anyone solved mine

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