Items tagged with odes


Hello friends!

I have one question, whenever I solved system of ODEs using numerical solution (bilton command i.e., dsolve(dsys1, numeric, output = listprocedure, range = 0 .. 1)), its accutacy always like 10 or 12 digits not above at all. I want to how i improve the accuracy. I am waiting your postive answer.

Hello! Hope everyone would be fine. I want to solve the following system of ODEs please help to find the numerical solution

N := .6; alpha := .4; beta := .1; Nt := .2; Pr := .5; Nb := .1; s := .2; lambda[1] := 1; delta := .5; gm := 1; Sc := 1:L:=1:

Eq1 := (alpha*s+1)*(diff(F(eta), eta, eta, eta))-(F(eta)+(1/2)*s*eta)*(diff(F(eta), eta, eta))+((1/2)*(diff(F(eta), eta))-s)*(diff(F(eta), eta))-2*(G(eta)^2-(1-gm)^2)-2*lambda[1]*(H(eta)+N*Y(eta))-(alpha+beta-(1/4)*delta*(diff(F(eta), eta, eta, eta)))*(diff(F(eta), eta, eta))^2-(alpha-2*beta)*(diff(F(eta), eta))*(diff(F(eta), eta, eta, eta))-(2*(alpha-beta-(1/4)*delta*(diff(F(eta), eta, eta, eta))))*(diff(G(eta), eta))^2-(2*(alpha-(1/4)*delta*(diff(F(eta), eta, eta))))*G(eta)*(diff(G(eta), eta, eta)) = 0; Eq2 := (alpha*s+1)*(diff(G(eta), eta, eta))-F(eta)*(diff(G(eta), eta))+G(eta)*(diff(F(eta), eta))+s*(1-gm-G(eta)-(1/2)*eta*(diff(G(eta), eta)))-(1/2)*alpha*s*eta*(diff(G(eta), eta, eta, eta))+((3/2)*alpha+beta)*G(eta)*(diff(F(eta), eta, eta, eta))-((1/2)*alpha+beta)*(diff(F(eta), eta))*(diff(G(eta), eta, eta))-delta*((diff(F(eta), eta, eta))^2+6*(diff(G(eta), eta))^2)*(diff(G(eta), eta, eta)) = 0; Eq3 := (diff(H(eta), eta, eta))/Pr-F(eta)*(diff(H(eta), eta))+(1/2)*H(eta)*(diff(F(eta), eta))-s*(2*H(eta)+(1/2)*eta*(diff(H(eta), eta)))+Nb*(diff(H(eta), eta))*(diff(Y(eta), eta))+Nt*(diff(H(eta), eta))^2 = 0; Eq4 := (diff(Y(eta), eta, eta))/Sc-F(eta)*(diff(Y(eta), eta))+(1/2)*Y(eta)*(diff(F(eta), eta))-s*(2*Y(eta)+(1/2)*eta*(diff(Y(eta), eta)))+Nt*(diff(H(eta), eta, eta))/Nb = 0;

IC1 := F(0) = 0, (D(F))(0) = 0, G(0) = gm, H(0) = 1, Y(0) = 1; IC2 := (D(F))(L) = 0, G(L) = 1-gm, (D(G))(L) = 0, H(L) = 0, Y(L) = 0; dsys1 := {Eq1, Eq2, Eq3, Eq4, IC1, IC2}; dsol1 := dsolve(dsys1, numeric, output = listprocedure, range = 0 .. L);

dsol1f := subs(dsol1, F(eta));

dsol1g := subs(dsol1, G(eta)); dsol1h := subs(dsol1, H(eta)); dsol1y := subs(dsol1, Y(eta));

With my best regards and sincerely.

Hello! I am facing the problem to making the grahp of system of ODEs in the attached file from eta=-1..1. Please see the attachment and fixed it. I will be waiting your positive response.

With my best regards and sincerely.

Muhammad Usman

School of Mathematical Sciences 
Peking University, Beijing, China


Mob #: 0086-13001903838

Hi there, fellow primers, it's good to be back after almost 5 years! I just want to share a worksheet on Numerov's algorithm in Maple using procedures as I've recently found out that google could not find any Maple procedure that implements Numerov's algorithm to solve ODEs.   Reference.pdf 

Hi everyone

When I solve these nonlinear ODEs, there is this problem i.e. Highlighted in yellow, in my solution. How can I solve it?


thanks a million!

i've got a list of 6 ODEs with 6 initial conditions:

MH,MS,M,a,G,e,afb are just constants

Eqns2 := diff(xH(t), t) = vxH(t),
            diff(vxH(t), t) = -G*M*xH(t)/(xH(t)^2+yH(t)^2)^(3/2),
            diff(yH(t), t) = vyH(t),
            diff(vyH(t), t) = -G*M*yH(t)/(xH(t)^2+yH(t)^2)^(3/2),

            diff(theta(t), t) = omega(t),

            diff(omega(t), t) = -G*MS*afb^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)^(5/2):

ICs2 := xH(0) = a*(1+e), vxH(0) = 0, vyH(0) = sqrt(G*M*(1-e)/(a*(1+e))), yH(0) = 0, 0 < theta(0), theta(0) <= Pi,        omega(0) = 10*Pi/T_H:

soln2 := dsolve({Eqns2, ICs2}, {omega(t), theta(t), vxH(t), vyH(t), xH(t), yH(t)}, numeric)

But it doesn't solve it , but instead displays this error message:

Error, (in dsolve/numeric/process_input) system must be entered as a set/list of expressions/equations

Can someone find a syntax error or a typo that would explain this?


I have been using MapleSoft since 2013 to solve mathematical problem. However, I could not solve the following set of differential equations.  Would you please, solve the problem and return the file how you solve it? Thanks in advance.

Dear collegues

Hope you are fine

I wrote a code to solve a system of ODEs.

The code solve the problem for higher values of parameter NBT>=5. When I decrease it to NBT=0.2, the code didnt converge. I did my best but I couldnt get the results.

I would be most grateful if you help me at this problem

The code is attached

Thank you



Hi to all

I had solve a set of ODEs using rkf45 method and I had plot it's Diagram now I need to have area under my diagram.what should I do? what is code?


I am trying to see how do I have initial conditions in a system of differential equations. This is an example problem, which doesn't work. What is wrong? Thank you.

plz help me, how do i solve singular ODEs of lane Emden type equation for homotopy analysis method in maple? there is arising an arror, invalid fraction



Eq1 := diff(f(eta), eta, eta, eta)+f(eta)*(diff(f(eta), eta, eta))-(diff(f(eta), eta))^2-M^2*(diff(f(eta), eta))+B(f(eta)*(diff(f(eta), eta, eta))*(diff(f(eta), eta))-f(eta)^2*(diff(f(eta), eta, eta, eta))) = 0;

Eq2 := (diff(theta(eta), eta, eta))/Pr+f(eta)*(diff(theta(eta), eta))-2*(diff(f(eta), eta))*theta(eta) = 0;

Pr := 1

M := 1

S := 0

epsilon := 1

blt := 10

bcs1 := f(0) = S, (D(f))(0) = epsilon, (D(f))(blt) = 0;

bcs2 := theta(0) = 1, theta(blt) = 0;

L := [0, .2, .4, .6, .8, 1.2];

for k to 6 do R := dsolve(eval({Eq1, Eq2, bcs1, bcs2}, B = L[k]), [f(eta), theta(eta)], numeric, output = listprocedure); X1 || k := rhs(R[3]); X2 || k := rhs(R[4]); Y1 || k := rhs(R[5]); Y2 || k := -rhs(R[6]) end do:

print([(X2 || (1 .. 6))(0)])

Good day everyone,

please how can one solve this pde in terms of Bessel function or any other analytic solution with the plot.

See the file



Restrict calculation to real numbers.

Using y' = u, express the oscillator equation: y" + 3y' + 2y = cos(t) as a first order system. 

Plot an approximate solution curve for the specified initial conditions.

[x0=5, y0=1],[x0=-2, y0=-4],[x0=0, y0=.1],

This is what i have so far but i am not sure if its correct.

Eulers modified method: 


x[0] := 0;

y[0] := 5;


h := .1;

for n to 100 do

x[n] := x[n-1]+h*(x[n-1]+y[n-1]);

k1 := x[n-1]+y[n-1];

k2 := h*k1+x[n]+y[n-1];

k := 1/2*(k1+k2);

y[n] := h*k+y[n-1]

end do;

data := [seq([x[n], y[n]], n = 0 .. 100)];
G1 := plot(data, style = point, color = "blue");

hi , kindly guide me how to draw combine graphs for velocity profile at different values of one parameter.  For example we have 3rd order ODE and A is parameter that is multiple of equation. now we want to see the effects of that parameter on this 3rd  order ODE.  Now  how can i sketch the  combine graph of Df(o) at A=1, 2, 3. (for example.)



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