# A power series method for solving ordinary and partial differentials equations motivated by domain growth

## TL;DR

This paper introduces a power series approach for solving various ordinary and partial differential equations, demonstrated through multiple examples including linear and nonlinear cases, with boundary conditions and general solutions provided.

## Contribution

The paper presents a novel power series method applicable to both ordinary and partial differential equations, including nonlinear and boundary value problems.

## Key findings

- Successfully solves diverse differential equations using the power series method
- Demonstrates applicability to linear and nonlinear PDEs and ODEs
- Provides solutions with boundary conditions and general forms

## Abstract

In this work we present a power series method for solving ordinary and partial differential equations. To demonstrate our method we solve a system of ordinary differential equations describing the movement of a random walker on a one-dimensional lattice, two nonlinear ordinary differential equations, a wave and diffusion equation (linear partial differential equations), and a nonlinear partial differential equation (quasilinear). The inclusion of boundary conditions and the general solutions to other equations of interest are included in the Supplementary material.