Symbolic Iterative Solution of Boundary Value Problems for Partial Differential Equations

TL;DR

This paper presents a symbolic iterative method combining Picard iteration and auxiliary variables for solving boundary value problems of partial differential equations, emphasizing simplicity, efficiency, and high accuracy.

Contribution

The paper introduces a novel symbolic iterative approach that simplifies and enhances the accuracy of solving PDE boundary value problems.

Findings

Method is easy to implement and computationally efficient

Produces highly accurate approximate solutions

Effective for a range of PDE boundary value problems

Abstract

In this article we introduce a simple straightforward and powerful method involving symbolic manipulation, Picard iteration, and auxiliary variables for approximating solutions of partial differential boundary value problems. The method is easy to implement, computationally efficient, and it is highly accurate. The output of the method is a function that approximates the exact solution.