Hello,

the simple answer is that you should not even try to do it. Picard iterative method is essentially an application of the fixed point theorem to the reformulation of an Ordinary Differential Equation (ODE) as an equivalent integral equation. The Picard iterative method can be used to prove AT A THEORETICAL LEVEL that the fixed point (that is, the solution) exists, at least over some short time interval. In practice, computing the solution in that way would be very difficult if not simply crazy. Solutions of ODE systems are best approximated by finite difference or other discretization methods (some of the most common are for example Runge Kutta methods).

Best regards

Luca

Thanks sir i really appreciate your kind gesture. I am a master student at the University of Lagos, Lagos Nigeria. My research is comparison between picard iterative method and Adomian Decomposition Method. So i was trying to look how i can compare a system of differential equation using Adomian decomposition and Picard iterative method. Thanks for your response it helps 

By Picard multi-dimensional method

can u please tell me more about picard multi-dimensional method and text that can help me?

If you have no choice, I have a "starting point" for you: R. Rach, On the Adomian (decomposition) method and comparisons with Picard’s method, J Math Anal. Appl 128 (1987), 480–483. It is for a single equation, but you can follow the papers citing the recommended one.

Here you have more: Carothers, David, et al. "An overview of the modified Picard Method." Department of Mathematics and Statistics, Physics, James Madison University, Harrisonburg, Report VA22807 (2004), or: Carothers, David, et al. "An overview of the modified Picard Method." Department of Mathematics and Statistics, Physics, James Madison University, Harrisonburg, Report VA22807 (2004).

and here: Bellomo, N., and D. Sarafyan. "On Adomian's decomposition method and some comparisons with Picard's iterative scheme." Journal of mathematical analysis and applications 123.2 (1987): 389-400.

Thanks It helps

I suggest you Picard-Green and Picard-Mann methods which and newly introduced methods.