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Dear guys!

I want to solve this system:

> c := 1: RC := 0.03: h := 1: m := 0.3:

> a := H(z)^2/(1+z)-h^2*(m*(1+z)^2+2*RC/(1+z));

> ode1 := diff(H(z),z) = (H(z)^4/((1+z)^2)+m*(1+z)*h^2*H(z)^2-2*m^2*h^4*(1+z)^4)/(2*H(z)*a) - (2*H(z)*h^2*RC)/(a*(1+z)^2) + (2*RC*h^2*(1+z)/(c*H(z)^2*a))*(H(z)^2/(1+z)^2-(H(z)^2/(1+z)-m*h^2*(1+z)^2)^2/(4*RC*h^2))^(3/2):

> ode2 := diff(M(z),z)=3*M(z)/(1+z)-2*M(z)*diff(H(z),z)/H(z):

> sys := {ode1, ode2}:

And so with this provocative title, "pushing dsolve to its limits" I want to share some difficulties I've been having in doing just that. I'm looking at a dynamic system of 3 ODEs. The system has a continuum of stationary points along a line. For each point on the line, there exist a stable (center) manifold, also a line, such that the point may be approached from both directions. However, simulating the converging trajectory has proven difficult.

I have simulated as...

Hello all,

 Is any anyone know how good is maple numeric stiff ode solver (stiff=true) ? What i mean is how many stiff ode's it can handle at a given time. I am having a hardtime solving a system of ode's (say 300 stiff ode's). Is there any other numeric stiff ode solver in maple that can handle large number of ode's?

I used islode advanced numeric solver for stiff ode's and it also has some limitations on the number of ode's and moreover it is slow.

Hi all,

 I am having a very hard time with numerical stability. I am solving system of ode's (7-coupled ode's) using dsolve(stiff) and then using spline function for interpolation and finally solving system of pde's (2-coupled pde's) using pdsolve for one time step and solving all again for the next step. the solution is not stable and it requires very fine/small time step. Is there any procedure/method to improve the stability? 

 What is the stability criteria of dsolve...

Dear mapleprimes ODE enthusiasts,

I am analyzing a stiff 3D system characterizes by fast-slow dynamics. I believe I can show analytically that, for some parameter values, in a neighborhood of some critical points (where the system is stationary), the dynamic system has a local center manifold that is center-stable. I have simulated the system for different parameter values.I am interested in one particular trajectory. With a random set of initial values, the system...