Approximate Solutions of Nonlinear Heat Equation for Given Flow

TL;DR

This paper develops approximate solutions for a nonlinear heat equation with specific boundary conditions, analyzing their convergence to address a one-dimensional heat flow problem with a power-function boundary condition.

Contribution

It introduces a method for approximating solutions to a nonlinear heat equation with a power-function boundary flow and discusses their convergence properties.

Findings

Approximate solutions are constructed for the nonlinear heat equation.

Convergence of these solutions is analyzed and discussed.

The method provides a way to handle nonlinear boundary conditions.

Abstract

The one-dimensional problem of the nonlinear heat equation is considered. We assume that the heat flow in the origin of coordinates is the power function of time and the initial temperature is zero. Approximate solutions of the problem are given. Convergence of approximate solutions is discussed.