Items tagged with differential differential Tagged Items Feed

Dear all,

It's very convenient to define a DE or PDE through Differential Operator D, for example,

((D[1, 1]+D[1, 2]+D[2, 2])(z))(x, y) = exp(x)*sin(y)

Is it possible to realize Inverse Operator Method of Operator D? How to solve the following equation if we rewrite the pde through inverse operator method?

(z)(x, y)=((D[1, 1]+D[1, 2]+D[2, 2])^(-1))exp(x)*sin(y)

 

Thanks a lot.

I am a problem with solve differential equation, please help me: THANKS 

g := (y^2-1)^2; I4 := int(g^4, y = -1 .. 1); I5 := 2*(int(g^3*(diff(g, y, y)), y = -1 .. 1)); I6 := int(g^3*(diff(g, y, y, y, y)), y = -1 .. 1); with(Student[Calculus1]); I10 := ApproximateInt(6/(1-f(x)*g)^2, y = -1 .. 1, method = simpson);

dsys3 := {I4*f(x)^2*(diff(f(x), x, x, x, x))+I5*f(x)^2*(diff(f(x), x, x))+I6*f(x)^3 = I10, f(-1) = 0, f(1) = 0, ((D@@1)(f))(-1) = 0, ((D@@1)(f))(1) = 0};

dsol5 := dsolve(dsys3, numeric, output = array([0.]));

              Error, (in dsolve/numeric/bvp) system is singular at left endpoint, use midpoint method instead

****************FORMAT TWO ********************************************************

g := (y^2-1)^2; I4 := int(g^4, y = -1 .. 1); I5 := 2*(int(g^3*(diff(g, y, y)), y = -1 .. 1)); I6 := int(g^3*(diff(g, y, y, y, y)), y = -1 .. 1); with(Student[Calculus1]); I10 := ApproximateInt(6/(1-f(x)*g)^2, y = -1 .. 1, method = simpson);
dsys3 := {I4*f(x)^2*(diff(f(x), x, x, x, x))+I5*f(x)^2*(diff(f(x), x, x))+I6*f(x)^3 = I10, f(-1) = 0, f(1) = 0, ((D@@1)(f))(-1) = 0, ((D@@1)(f))(1) = 0};

dsol5 := dsolve(dsys3, method = bvp[midrich], output = array([0.]));
%;
                                   Error, (in dsolve) too many levels of recursion

I DONT KNOW ABOUT THIS ERROR

PLEASE HELP ME

THANKS A LOT

 

Is it possible to solve piecewise differential equations directly instead of separating the pieces and solving them separately.

like for example if i have a two dimensional function f(t,x) whose dynamics is as follows:

dynamics:= piecewise((t,x) in D1, pde1, pde2); where D1 is some region in (t,x)-plane

now is it possible to solve this system with one pde call numerically?

pde(dynamics, boundary conditions, numeric); doesnot work

******************************************where d1 to d45 -kappa and chi are constant**********

dsys4 := {d1*h1(theta)+d2*(diff(h1(theta), theta, theta))+d3*(diff(h2(theta), theta))+d4*(diff(h2(theta), theta, theta, theta))+d5*h3(theta)+d6*(diff(h3(theta), theta, theta))+d7*(diff(h1(theta), theta, theta, theta, theta)) = 0, d8*h2(theta)+d9*(diff(h2(theta), theta, theta, theta, theta))+d10*(diff(h2(theta), theta, theta))+d11*(diff(h1(theta), theta))+d12*(diff(h1(theta), theta, theta, theta))+d13*(diff(h3(theta), theta))+d14*(diff(h3(theta), theta, theta, theta)) = 0, h3(theta)^5*(d16+ln(h3(theta))^2*d15+2*ln(h3(theta))*d17)+(diff(h3(theta), theta, theta))*h3(theta)^4*(d19+ln(h3(theta))^2*d18+2*ln(h3(theta))*d20)+(diff(h3(theta), theta, theta, theta, theta))*h3(theta)^4*(d22+ln(h3(theta))^2*d21+2*ln(h3(theta))*d23)+h1(theta)*h3(theta)^4*(d25+ln(h3(theta))^2*d24+2*ln(h3(theta))*d26)+(diff(h1(theta), theta, theta))*h3(theta)^4*(d28+ln(h3(theta))^2*d27+2*ln(h3(theta))*d29)+(diff(h2(theta), theta))*h3(theta)^4*(d31+ln(h3(theta))^2*d30+2*ln(h3(theta))*d32)+(diff(h2(theta), theta, theta, theta))*h3(theta)^4*(d34+ln(h3(theta))^2*d33+2*ln(h3(theta))*d35)+h3(theta)^4*(d37+ln(h3(theta))^2*d36+2*ln(h3(theta))*d38)+h3(theta)^4*(diff(h2(theta), theta, theta, theta, theta, theta, theta))*(d40+ln(h3(theta))^2*d39+2*ln(h3(theta))*d41)-beta*h3(theta)^3*d42-chi*ln(h3(theta))^2*d43/kappa-chi*d45/kappa-2*chi*ln(h3(theta))*d44/kappa = 0, h1(0) = 0, h1(1) = 0, h2(0) = 0, h2(1) = 0, h3(0) = 1, h3(1) = 1, ((D@@1)(h1))(0) = 0, ((D@@1)(h1))(1) = 0, ((D@@1)(h2))(0) = 0, ((D@@1)(h2))(1) = 0, ((D@@1)(h3))(0) = 0, ((D@@1)(h3))(1) = 0, ((D@@2)(h3))(0) = 0, ((D@@2)(h3))(1) = 0}; dsol6 := dsolve(dsys4, 'maxmesh' = 600, numeric, output = listprocedure)

Hi,

I would like a plot of the solution of this differential equation : diff(phi(x),x,x)=phi(x)*(Ep(x)-E) with for example Ep(x)=(1-exp-(x-2))^2 and E=0.5

 

So :

>restart;with(plots); xith(DEtools);

>Ep:=x->(1-exp-(x-2))^2;E:=0.5;

>sol:=dsolve({eq,phi(o)=0,D(phi)(0)=0},type=numeric,range=0..10);

>odeplot(sol);

but nothing appear in the plot except axes

Thanks for answer

 

hi.i encountered this erroe  [Error, (in dsolve/numeric/bvp/convertsys) unable to convert to an explicit first-order system] with solving set of differential equation.please help me.thanks a lot  

dsys3 := {`1`*h1(theta)+`1`*(diff(h1(theta), theta, theta))+`1`*(diff(h2(theta), theta))+`1`*(diff(h2(theta), theta, theta, theta))+`1`*h3(theta)+`1`*(diff(h3(theta), theta, theta))+`1`*(diff(h1(theta), theta, theta, theta, theta)) = 0, `1`*h2(theta)+`1`*(diff(h2(theta), theta, theta, theta, theta))+`1`*(diff(h2(theta), theta, theta))+`1`*(diff(h1(theta), theta))+`1`*(diff(h1(theta), theta, theta, theta))+`1`*(diff(h3(theta), theta))+`1`*(diff(h3(theta), theta, theta, theta)) = 0, h3(theta)^5*(`1`+ln(h3(theta))^2*`1`+2*ln(h3(theta))*`1`)+(diff(h3(theta), theta, theta))*h3(theta)^4*(`1`+ln(h3(theta))^2*`1`+2*ln(h3(theta))*`1`)+(diff(h3(theta), theta, theta, theta, theta))*h3(theta)^4*(`1`+ln(h3(theta))^2*`1`+2*ln(h3(theta))*`1`)+h1(theta)*h3(theta)^4*(`1`+ln(h3(theta))^2*`1`+2*ln(h3(theta))*`1`)+(diff(h1(theta), theta, theta))*h3(theta)^4*(`1`+ln(h3(theta))^2*`1`+2*ln(h3(theta))*`1`)+(diff(h2(theta), theta))*h3(theta)^4*(`1`+ln(h3(theta))^2*`1`+2*ln(h3(theta))*`1`)+(diff(h2(theta), theta, theta, theta))*h3(theta)^4*(`1`+ln(h3(theta))^2*`1`+2*ln(h3(theta))*`1`)+h3(theta)^4*(`1`+ln(h3(theta))^2*`1`+2*ln(h3(theta))*`1`)+h3(theta)^4*(diff(h2(theta), theta, theta, theta, theta, theta, theta))*(`1`+ln(h3(theta))^2*`1`+2*ln(h3(theta))*`1`)-beta*h3(theta)^3*`1`-chi*ln(h3(theta))^2*`1`/kappa-chi*`1`/kappa-2*chi*ln(h3(theta))*`1`/kappa = 0, h1(0) = 0, h1(1) = 0, h2(0) = 0, h2(1) = 0, h3(0) = 1, h3(1) = 1, ((D@@1)(h1))(0) = 0, ((D@@1)(h1))(1) = 0, ((D@@1)(h2))(0) = 0, ((D@@1)(h2))(1) = 0, ((D@@1)(h3))(0) = 0, ((D@@1)(h3))(1) = 0, ((D@@2)(h3))(0) = 0, ((D@@2)(h3))(1) = 0}; dsol5 := dsolve(dsys3, 'maxmesh' = 600, numeric, output = listprocedure);
%;
Error, (in dsolve/numeric/bvp/convertsys) unable to convert to an explicit first-order system

 

 Hi all,

i want to solve a system of differential equations in maple with "dsolve, numeric",

i got th error message: "Error, (in f) unable to store in Matrix ..."

what is the problem?

thanks a lot

Hello fellow maple users,im new to the software,im trying to solve a differential system but it dosent work

 

This is the system :

DE1 := diff(Y(t), t) = 5*Y(t)*ln(b(t)/Y(t))-5*Y(t)

DE2 := diff(b(t), t) = 5*b(t)*Y(t)^(3/2)-5*Y(t)

 

Thank you for your help !

hi everyone,i have two questions,
1. i have a problem with select command? 

restart:

eq[1]:=diff(a[1](x),x$2)+diff(a[1](x),x$1)*diff(a[2](x),x$1)+diff(a[1](x),x$2)*diff(a[2](x),x$2)+diff(a[3](x),x$1)+diff(a[1](x),x$1)*diff(a[2](x),x$2)+diff(a[1](x),x$2)*diff(a[3](x),x$1);

diff(diff(a[1](x), x), x)+(diff(a[1](x), x))*(diff(a[2](x), x))+(diff(diff(a[1](x), x), x))*(diff(diff(a[2](x), x), x))+diff(a[3](x), x)+(diff(a[1](x), x))*(diff(diff(a[2](x), x), x))+(diff(diff(a[1](x), x), x))*(diff(a[3](x), x))

(1)

# how can i select the differentials which are of second order ? without using the function names , for example i do not want to use this :

select(has,eq[1],[seq](diff(a[i](x),x$2),i=1..3));

diff(diff(a[1](x), x), x)+(diff(diff(a[1](x), x), x))*(diff(diff(a[2](x), x), x))+(diff(a[1](x), x))*(diff(diff(a[2](x), x), x))+(diff(diff(a[1](x), x), x))*(diff(a[3](x), x))

(2)

#i just want maple to select the second order differentials,without knowing its name # just beacuse it is of second order,how can i do this !?

2. how i can select the parts which their addition of differential oreder,are the same ? for example,the second expression in eq[1] has the addition order of 2,third has 4 and ... how can isolate addition order ? tnx in advance . 

Download select.mw

Hi,

how can I solve a set of first order, coupled, non-linear and inhomogeneous differential equations using MAPLE 12.

I have a differential equation system x'(t)=f1(k,t)*x(t)+f2(k,t)*y(t), x'(t)=g1(k,t)*x(t)+g2(k,t)*y(t) with initial condition x(0)=1 and y(0)=1. Here k is a parameter, f1, f2,g1, g2 are certain functions of k and t. I used dsolve and set k to be a parameter to solve the system numerically which gives you a procedure output. If I fixed k to be a specific numerical number, then I can use odeplot to plot x(t) VS t.

Now I set a range for k, say k=0..10. And I want to plot x VS (t,k) which is a 3D graph. How can I do this?

Hi all,

 

As we know that the differential of conjugate(z) is non-analytic.

But it seems that the diff gives the solution about the complex function conjugate(z)

 

What does it mean?

Hello Hello everybody 
   I have to solve the following differential equation numerically 


``

 

restart:with(plots):

mb:=765 : mp:=587 : Ib:=76.3*10^3 : Ip:=7.3*10^3 : l:=0.92 : d:=10: F:=490: omega:=0.43 :

eq1:=(mp+mb)*diff(x(t),t$2)+mp*(d*cos(theta(t))+l*cos(alpha(t)+theta(t)))*diff(theta(t),t$2)+mp*l*cos(alpha(t)+theta(t))*diff(alpha(t),t$2)+mp*(d*diff(theta(t),t)^2*sin(theta(t))+l*(diff(theta(t),t)+diff(alpha(t),t))^2*sin(alpha(t)+theta(t)))-F*sin(omega*t)=0;

1352*(diff(diff(x(t), t), t))+587*(10*cos(theta(t))+.92*cos(alpha(t)+theta(t)))*(diff(diff(theta(t), t), t))+540.04*cos(alpha(t)+theta(t))*(diff(diff(alpha(t), t), t))+5870*(diff(theta(t), t))^2*sin(theta(t))+540.04*(diff(theta(t), t)+diff(alpha(t), t))^2*sin(alpha(t)+theta(t))-490*sin(.43*t) = 0

(1)

eq2:=(mp+mb)*diff(z(t),t$2)-mp*d*(sin(theta(t)+alpha(t))+sin(theta(t)))*diff(theta(t),t$2)-mp*l*sin(alpha(t)+theta(t))*diff(alpha(t),t$2)+mp*(d*diff(theta(t),t)^2*cos(theta(t))+l*(diff(theta(t),t)+diff(alpha(t),t))^2*cos(alpha(t)+theta(t)))+9.81*(mp+mb)-F*sin(omega*t)=0;

1352*(diff(diff(z(t), t), t))-5870*(sin(alpha(t)+theta(t))+sin(theta(t)))*(diff(diff(theta(t), t), t))-540.04*sin(alpha(t)+theta(t))*(diff(diff(alpha(t), t), t))+5870*(diff(theta(t), t))^2*cos(theta(t))+540.04*(diff(theta(t), t)+diff(alpha(t), t))^2*cos(alpha(t)+theta(t))+13263.12-490*sin(.43*t) = 0

(2)

eq3:=mp*(d*cos(theta(t))+l*cos(alpha(t)+theta(t)))*diff(x(t),t$2)-mp*(l*sin(theta(t)+alpha(t))+d*sin(theta(t)))*diff(z(t),t$2)+(Ip+Ib+mp*(d^2+l^2)+2*mp*d*l*cos(alpha(t)))*diff(theta(t),t$2)+[Ip+mp*l^2+mp*d*l*cos(alpha(t))]*diff(alpha(t),t$2)-mp*sin(alpha(t))*(l*d*diff(alpha(t),t)^2-l*d*(diff(alpha(t),t)+diff(theta(t),t))^2)+mp*9.81*l*sin(alpha(t)+theta(t))+mp*9.81*d*sin(theta(t))=0;

587*(10*cos(theta(t))+.92*cos(alpha(t)+theta(t)))*(diff(diff(x(t), t), t))-587*(.92*sin(alpha(t)+theta(t))+10*sin(theta(t)))*(diff(diff(z(t), t), t))+(142796.8368+10800.80*cos(alpha(t)))*(diff(diff(theta(t), t), t))+[7796.8368+5400.40*cos(alpha(t))]*(diff(diff(alpha(t), t), t))-587*sin(alpha(t))*(9.20*(diff(alpha(t), t))^2-9.20*(diff(theta(t), t)+diff(alpha(t), t))^2)+5297.7924*sin(alpha(t)+theta(t))+57584.70*sin(theta(t)) = 0

(3)

eq4:=mp*l*cos(alpha(t)+theta(t))*diff(x(t),t$2)-mp*l*sin(alpha(t)+theta(t))*diff(z(t),t$2)+(Ip+mp*l^2+mp*d*l*cos(alpha(t)))*diff(theta(t),t$2)+(Ip+mp*l^2)*diff(alpha(t),t$2)-mp*9.81*l*sin(alpha(t)+theta(t))+l*d*mp*diff(theta(t),t$1)^2*sin(alpha(t))=0;

540.04*cos(alpha(t)+theta(t))*(diff(diff(x(t), t), t))-540.04*sin(alpha(t)+theta(t))*(diff(diff(z(t), t), t))+(7796.8368+5400.40*cos(alpha(t)))*(diff(diff(theta(t), t), t))+7796.8368*(diff(diff(alpha(t), t), t))-5297.7924*sin(alpha(t)+theta(t))+5400.40*(diff(theta(t), t))^2*sin(alpha(t)) = 0

(4)

CI:= x(0)=0,z(0)=0,theta(0)=0,alpha(0)=0,D(x)(0)=0,D(alpha)(0)=0,D(z)(0)=0,D(theta)(0)=0;

x(0) = 0, z(0) = 0, theta(0) = 0, alpha(0) = 0, (D(x))(0) = 0, (D(alpha))(0) = 0, (D(z))(0) = 0, (D(theta))(0) = 0

(5)

solution:=dsolve([eq1,eq2,eq3,eq4, CI],numeric);

Error, (in f) unable to store '[0.]/(0.17571268341557e16+[-0.25659510610770e15])' when datatype=float[8]

 

 

 

I don't know why it says : Error, (in f) unable to store '[0.]/(0.17571268341557e16+[-0.25659510610770e15])' when datatype=float[8]

 

Help pleaase!

thank you !!!

Download systéme_complet.mw

 

Hello all,

I'm an engineering student working on bicycle shifting. After an dynamic study i encounter the equation:

E:=5.37*theta12(t)=C*(diff(theta12(t),[t$2])+diff(theta10(t),[t$2]))+247.2*[diff(theta10(t),[t$2])*(-6.53*cos(theta12(t))+8.51*sin(theta12(t)))+diff(theta10(t),t)*diff(theta12(t),t)*(6.53*sin(theta12(t))+8.51*cos(theta12(t)))]-247.2*diff(theta10(t),t)*(-diff(theta12(t),t)+diff(theta10(t),t))*(-6,53*sin(theta12(t))-8,51*cos(theta12(t)));


where C is a real constant

More exactly, i would need to find a formule for theta12 using the succesive derivatives of theta10.

I heard that i need to search a numerical solution but,up to now, don't succeed to solve it.

I'm open to all idea.

Thanks

How can I solve a differential equation set of the type,

dy(x)/dx +y^2 =P(x); dP(x)/dx = R(P) numerically

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