Numerical methods that need a guess/approximate solutions

[Nate_CU]

Hello everyone! I am currently playing with an old analog computer, which could solve time-dependent ODE/PDEs pretty fast, without time-stepping. But the problem with analog computer's solutions is that they are not very accurate. I am very curious that is there any numerical method/solver which can take an approximate solution (over the time domain) to further process it, and generate a more accurate solution??

Thanks in advance!

 

[Dr. Courtney]

I can't think of any general ones, but applications of the least action principles should be able to search around an approximate solution to find an exact solution more quickly.

I've also written code for searching out periodic orbits of chaotic systems. Having approximations to begin with would make the process faster.

 

[Nate_CU]

I can't think of any general ones, but applications of the least action principles should be able to search around an approximate solution to find an exact solution more quickly.

I've also written code for searching out periodic orbits of chaotic systems. Having approximations to begin with would make the process faster.

Dear Dr. Courtney,

Thanks for your reply! I have never heard of "least action principles" numerical solvers for solving ODEs. (Sorry about my weak math background!) Is this a popular way to solve ODEs?

Analog computers can also provide solutions of ODEs describing chaotic systems. Can you provide me more details on your codes? What initial information do you need to get started? Thank you!

 

[MaziyarTorkfar]

hello every one
i have a differential equation:
Y''(x)+A*y(x)*(1+B*(y(x)^0.687))=0
i solve it numerically but i need a function for it unfortunately its give me complex number.
i need some program that can estimate complex plot and number
thank you