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i have run higer order nonlinear ode bvp

but cant solve the error

please help me

NULL

restart

with(plots)

Pr := .71; beta := .5; alpha := .1; S := .1; Du := .1; Nb := .1; Nt := .1; Sc := .67; Sr := .1; omega := 1.0; Lb := 1.0; Pe := 1.0; delta := 1.0; Nc := 1.0; p := .1; q := 5; r := 5; s := 5; a := 1; b := 2; epsilon := .1

Eq1 := (101-100*lambda)*(diff(f(eta), `$`(eta, 3)))-theta(eta)*beta*(diff(f(eta), `$`(eta, 2)))/(1+theta(eta)*beta)+(1+theta(eta)*beta)*f(eta)*(diff(f(eta), `$`(eta, 2)))-(1+theta(eta)*beta)*(diff(f(eta), eta))^2-(M-alpha)*(1+theta(eta)*beta)*(diff(f(eta), eta))

(101-100*lambda)*(diff(diff(diff(f(eta), eta), eta), eta))-.5*theta(eta)*(diff(diff(f(eta), eta), eta))/(1+.5*theta(eta))+(1+.5*theta(eta))*f(eta)*(diff(diff(f(eta), eta), eta))-(1+.5*theta(eta))*(diff(f(eta), eta))^2-(M-.1)*(1+.5*theta(eta))*(diff(f(eta), eta))

(1)

Eq2 := (1+epsilon*theta(eta))*(diff(theta(eta), `$`(eta, 2)))+f(eta)*(diff(theta(eta), eta))+epsilon*(diff(theta(eta), eta))^2+Pr*S*theta(eta)+Pr*Du*(diff(phi(eta), `$`(eta, 2)))+Pr*Nb*(diff(theta(eta), eta))*(diff(phi(eta), eta))+Pr*Nt*(diff(theta(eta), eta))^2

(1+.1*theta(eta))*(diff(diff(theta(eta), eta), eta))+f(eta)*(diff(theta(eta), eta))+.171*(diff(theta(eta), eta))^2+0.71e-1*theta(eta)+0.71e-1*(diff(diff(phi(eta), eta), eta))+0.71e-1*(diff(theta(eta), eta))*(diff(phi(eta), eta))

(2)

Eq3 := (diff(phi(eta), `$`(eta, 2)))/Sc+f(eta)*(diff(phi(eta), eta))-omega*(diff(theta(eta), eta))*(diff(phi(eta), eta))-omega*(diff(theta(eta), `$`(eta, 2)))*phi(eta)-delta*phi(eta)+omega*Nc*(diff(theta(eta), `$`(eta, 2)))+Sr*(diff(theta(eta), `$`(eta, 2)))

1.492537313*(diff(diff(phi(eta), eta), eta))+f(eta)*(diff(phi(eta), eta))-1.0*(diff(theta(eta), eta))*(diff(phi(eta), eta))-1.0*(diff(diff(theta(eta), eta), eta))*phi(eta)-1.0*phi(eta)+1.10*(diff(diff(theta(eta), eta), eta))

(3)

Eq4 := diff(chi(eta), `$`(eta, 2))+Lb*f(eta)*(diff(chi(eta), eta))-Pe*(diff(phi(eta), eta))*(diff(chi(eta), eta))-Pe*(diff(phi(eta), `$`(eta, 2)))*chi(eta)

diff(diff(chi(eta), eta), eta)+1.0*f(eta)*(diff(chi(eta), eta))-1.0*(diff(phi(eta), eta))*(diff(chi(eta), eta))-1.0*(diff(diff(phi(eta), eta), eta))*chi(eta)

(4)

VM := [0., .5, 1.0]

etainf := 9

bcs := f(0) = 0, (D(f))(0) = p*(D@@2)(f)*0, theta(0) = 1+q*(D(theta))(0), phi(0) = 1+r*(D(phi))(0), chi(0) = 1+s*(D(chi))(0), D(f)*etainf = b/a, theta(etainf) = 0, phi(etainf) = 0, chi(etainf) = 0

f(0) = 0, (D(f))(0) = 0., theta(0) = 1+5*(D(theta))(0), phi(0) = 1+5*(D(phi))(0), chi(0) = 1+5*(D(chi))(0), 9*D(f) = 2, theta(9) = 0, phi(9) = 0, chi(9) = 0

(5)

dsys := {Eq1, Eq2, Eq3, Eq4, bcs}

for i to 3 do M := VM[i]; dsol[i] := dsolve(dsys, numeric, continuation = lambda); print(M); print(dsol[i](0)) end do

 

 

 

 

 



thanks. I played around, and had problems implementing your ideas for one of the systems I'm interested in.I don't see a difference between this and what you had advised me on, but it gets an error.

any idea why?
or how to fix it?

thing1 := diff(B[1](t), t) = piecewise(t <= 500, 0.3e-2-(63/10000)*B[1](t)-(3/500)*B[2](t), -(3/10000)*B[1](t)):
thing2 := diff(B[1](t), t) = piecewise(t <= 500, 0.1e-1-(1/50)*B[1](t)-(13/625)*B[2](t), -(1/1250)*B[2](t)):
sol := dsolve({thing1, thing2, B[1](0) = 0, B[2](0) = 0}, {B[1](t), B[2](t)}, numeric, output = listprocedure); plots:-odeplot(sol, [B[1](t), B[2](t)], t = 450 .. 550);

Error, (in dsolve/numeric/DAE/explicit) unable to obtain the standard form of the DAE system due to the presence of leading dependent variables/derivatives in the piecewise: piecewise(t <= 500, 1/100-(1/50)*B[1](t)-(13/625)*B[2](t), -(1/1250)*B[2](t))-piecewise(t <= 500, 3/1000-(63/10000)*B[1](t)-(3/500)*B[2](t), -(3/10000)*B[1](t))
Error, (in plots/odeplot) curve is not fully specified in terms of the ODE solution, found additional unknowns {B[1](t), B[2](t)}


Hello

I have an SEIR model.

Equation 5 is for disease death but I would like to plot the cumulative numbers of disease death which will be the integral of Equation 5. I added the integral inside odeplot but it is not working. Any idea  about  how to compute the integral ?

Maple code is attached

Thank you

code.mw

PLEASE..!! CAN ANYONE HELP ME IN CODING ON MAPPLE 13 TO CHANGE PDE INTO ODE??

MY FUNCTION IS THIS

U[t, t]-U[t, t, x, x]-(aU[]-b*U[]^3)[x, x] = 0

Hi,

 

I have an issue calculating an electronics circuit with Maple, using units. I have a current source that I know, and I want to determin the voltage in a capacitor by solving an ODE (except that the current source is defined piecewise). And to make sure I have all the units and scales right, I use the standard unit package. All my variables have their units defined.

Except that Maple doesn't want to solve the equation. It seems to me that it assumes that the function I am trying to solve is unitless, and therefore refuses to solve. 

V__out := 3*Unit('kV');

C__out := 2*Unit('nF');
R__blead := 520*Unit('`k&Omega;`');

I__fly := proc (t) options operator, arrow; Unit('A')*piecewise(t < 3.25*Unit('us'), (1+(-1)*t/(3.25*Unit('us')))*.2, 0) end proc;

 

dsolve({I__fly(t*Unit('s'))-V__C(t*Unit('s'))/R__blead = C__out*(diff(V__C(t*Unit('s')), t)), V__C(0*Unit('s')) = V__out}, V__C(t*Unit('s')));
Error, (in Units:-Standard:-+) the units `A` and `S` have incompatible dimensions

 

Is there a way to make Maple assume the unit of what it's trying to solve ? I need it to understands that V__C is in Unit('V') ...

 

Thanks

 

See attached file and code

0. This is the differential equation I'm trying to do:

http://www.intmath.com/differential-equations/6-rc-circuits.php

https://i.imgur.com/zlVIisR.png

 

1. After you look at the above imgur link, could you help me with this error 

Error, (in Units:-Standard:-+) the units ``&Omega;`` and `1/F` have incompatible dimensions

  

2. Why does my solve ODE fail? 

 

See my code: 

test_maple.mw

using FDM or FEM rather than dsolve?

ode.docxode.docx

Hi, Im now trying to run my code. But it took like years to even getting the results. may I know any solutions on how to get faster results? Because I have run this code for almost 4 hours yet there is still 'Evaluating...' at the corner left. And when I tried to stop the program, it will stop at 'R1...'.

 

Digits := 18;
with(plots):n:=1.4: mu(eta):=(diff(U(eta),eta)^(2)+diff(V(eta),eta)^(2))^((n-1)/(2)):
Eqn1 := 2*U(eta)+(1-n)*eta*(diff(U(eta), eta))/(n+1)+diff(W(eta), eta) = 0;
Eqn2 := U(eta)^2-(V(eta)+1)^2+(W(eta)+(1-n)*eta*U(eta)/(n+1))*(diff(U(eta), eta))-mu(eta)*(diff(U(eta), eta, eta))-(diff(U(eta), eta))*(diff(mu(eta), eta)) = 0;
Eqn3 := 2*U(eta)*(V(eta)+1)+(W(eta)+(1-n)*eta*U(eta)/(n+1))*(diff(V(eta), eta))-mu(eta)*(diff(V(eta), eta, eta))-(diff(V(eta), eta))*(diff(mu(eta), eta)) = 0;
bcs1 := U(0) = 0, V(0) = 0, W(0) = 0;
bcs2 := U(4) = 0, V(4) = -1;
R1 := dsolve({Eqn1, Eqn2, Eqn3, bcs1, bcs2}, {U(eta), V(eta), W(eta)}, initmesh = 30000, output = listprocedure, numeric);
Warning, computation interrupted
for l from 0 by 2 to 4 do R1(l) end do;
plot1 := odeplot(R1, [eta, U(eta)], 0 .. 4, numpoints = 2000, color = red);

 

Thankyou in advance :)

Hello Everybody,

I was trying to apply the Newton-Raphon method("Newton" in maple) for the following problem to obtain the constants (c1...cM) without success.

eq[1] := -0.0139687 c[2] - 0.0132951 c[1] = 0
eq[2] := 24806.4 c[2] - 0.0139687 c[1] = 0

If anybody has experience with it or knows how to use it I would really appreciate your help.

 

Just to introduce the previous steps of calculations leading to the problem:To calculate the critical buckling force N and the shape of a rectangular uniformly loaded plate the governing diff. equation is the following

D11*w''''(x)+(2*D12+4*D66)*w''(x)''(y)+D22*w''''(y)+N*w''(x)=0

For the follwing solution of a boundary value problem(Boundary conditions:clamped-clamped: w(x=0,x=a)=0 & w'(x=0,x=a)=0) I applied the Ritz method:

w:=sum(c[i]*(cos(2*i*Pi*x/a)-1)),i=1..M)

Thus the Potential Energy P is:

P:=16537.6*c[2]^2-0.0139687*c[2]*c[1]+1033,60*c[1]^2-9.86960*N*c[2]^2-2.46740*N*c[1]^2

 deriving P to each constant c and setting them =0 leads to:

eq[1] := -0.0139687 c[2] + 2067.20 c[1] - 4.93480 N c[1] = 0
eq[2] := 33075.2 c[2] - 0.0139687 c[1] - 19.7392 N c[2] = 0

After calculating N=418,902  and feeding eq1 and eq 2,the follwing equations if two terms are considered:

eq[1] := -0.0139687 c[2] - 0.0132951 c[1] = 0
eq[2] := 24806.4 c[2] - 0.0139687 c[1] = 0

Everything I tried resulted in any c1 = c2 = 0 which is not  realistic. Maybe I made a mistake earlier.

Thanks a lot in advance.

Sam

 Plate_Buckling.mw

I have an ODE with L(x,y), which includes partial derivatives of L(x,y) and coefficients y,_y1 and _y1^2. I want to split this equation into seperate equations of these coefficients. So I can solve for the unknown variable L(x,y).

 

ODE:=diff(L(x,y),x,x)+2*_y1(x)*diff(L(x,y),x,y)+_y1(x)^2*diff(L(x,y),y,y)+y(x)/x*diff(L(x,y),x)+(y(x)*_y1(x)/x+_y1(x))*diff(L(x,y),y)-y(x)/x^2*L(x,y)=0;

Could someone help me? 

 

I am currently trying to use the coeffs command but not really getting anywhere.

 

Thank you.

I'm trying to find lypunov exponent for this  system of ODEs. I know I need to take the Jacobian but not sure if it's possible the way it's currently defined. If anyone could provide insight it would be much appreciated.

Eqns:= diff(omega(t),t)=-(G*MSat*beta^(2)*(xH(t)*sin(theta(t))-yH(t)* cos(theta(t)))*(xH(t)*cos(theta(t))+yH(t)*sin(theta(t))))/((xH(t)^(2)+yH(t)^(2))^(2.5)),diff(theta(t),t)=omega(t), diff(xH(t),t)=vxH(t),diff(vxH(t),t)=-(G*M*xH(t))/((xH(t)^(2)+yH(t)^(2))^(1.5)),diff(yH(t),t)=vyH(t),diff(vyH(t),t)=-(G*M*yH(t))/((xH(t)^(2)+yH(t)^(2))^(1.5)): ;

ICs := omega(0) = omega0, theta(0) = theta0, xH(0) = a*(1+e), yH(0) = 0, vxH(0) = 0, vyH(0) = sqrt(G*M*(1-e)/(a*(1+e)));

I want the exponent for omega, I  procedure that takes some initial conditions, changing just w0, and computes the long term value of omega. This plots a sort of bifurcation diagram. I'd like an estimate of the exponent to compare what I see. 

thanks for the help

ft

I don't know what is the problem with this. Please take a look at it. Any help is appreciated. Thanks.

restart

with(RealDomain)

[Im, Re, `^`, arccos, arccosh, arccot, arccoth, arccsc, arccsch, arcsec, arcsech, arcsin, arcsinh, arctan, arctanh, cos, cosh, cot, coth, csc, csch, eval, exp, expand, limit, ln, log, sec, sech, signum, simplify, sin, sinh, solve, sqrt, surd, tan, tanh]

(1)

with(Slode)

[DEdetermine, FPseries, FTseries, candidate_mpoints, candidate_points, dAlembertian_formal_sol, dAlembertian_series_sol, hypergeom_formal_sol, hypergeom_series_sol, mhypergeom_formal_sol, mhypergeom_series_sol, msparse_series_sol, polynomial_series_sol, rational_series_sol, series_by_leastsquare]

(2)

ODE := x*(diff(y(x), x, x))-(diff(y(x), x))-x*y(x)

x*(diff(diff(y(x), x), x))-(diff(y(x), x))-x*y(x)

(3)

SS := convert(sin(x), FormalPowerSeries)

Sum((-1)^k*x^(2*k+1)/factorial(2*k+1), k = 0 .. infinity)

(4)

FPseries(ODE = SS, y(x), v(n))

Error, the right-hand side of the differential equation must be a polynomial or a series in x

 

``

 

Download AA.mw

Dear all;

Good morning everyone.

I solve a simple ode, i want how can I write this program as procedure with output the two coefficient involved in the solution, after solving with ics. i.e coef:=dsolve(ode);  in my example I want as output [4, -1] .

 

restart:
ode:=diff(y(x),x,x)=3*diff(y(x),x)-2*y(x);
coef:=dsolve(ode);
ics:=y(0)=3, D(y)(0)=2;
dsolve({ics,ode});

with best regards

 

Hello,

I have two regimes. Each regime is characterized by system of state differential equations (diff(S(t), t), diff(K(t), t)) and co-state differential equations (diff(psi[S](t), t), diff(psi[Iota](t), t)) as follows: 

(1)

diff(S(t), t) = -eta*K(t)*S(t)/(w*N*(S(t)+K(t))), diff(K(t), t) = eta*K(t)*S(t)/(w*N*(S(t)+K(t)))-upsilon

diff(psi[S](t), t) = eta*K(t)^2*(psi[S](t)-psi[Iota](t))/(w*N*(S(t)+K(t))^2), diff(psi[Iota](t), t) = eta*S(t)^2*(psi[S](t)-psi[Iota](t))/(w*N*(S(t)+K(t))^2)

(2)

diff(S(t), t) = -eta*K(t)*S(t)/(w*N*(S(t)+K(t))), diff(K(t), t) = eta*K(t)*S(t)/(w*N*(S(t)+K(t)))

diff(psi[S](t), t) = eta*K(t)^2*(psi[S](t)-psi[Iota](t))/(w*N*(S(t)+K(t))^2), diff(psi[Iota](t), t) = eta*S(t)^2*(psi[S](t)-psi[Iota](t))/(w*N*(S(t)+K(t))^2)

The first regime is employed from 0 to t1 (where t1 is unknown) and then regime 2, from t1 to T. I know the initial values for the state variables of the first system at t=0, that is, S(0)=S0 and K(0)=K0, as well as boundary conditions for the co-state variables for regime 2 at t=T, that is, psi_S(T)=a and psi_I(T)=b. 

I also know that my unknown t1 should satisfy the algebraic equation: -c - psi_S(t1)=0, where psi_S(t1) is the solution of the co-state diff equation of the regime 2 at t=t1. 

My question is: If I assume that the systems have not analytical solution, how can I found unknown t1 numerically? Moreover, asssume that all other parameters, such as T, eta, upsilon and others are given.

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