Presenting a new method for the solution of nonlinear problems

TL;DR

This paper introduces a novel method combining Linear Delta Expansion with Lindstedt-Poincaré to improve solutions of oscillatory nonlinear problems, demonstrated on the Duffing equation.

Contribution

The paper presents a new hybrid approach that enhances the accuracy of nonlinear problem solutions beyond traditional Lindstedt-Poincaré methods.

Findings

Significant improvement in approximation accuracy for the Duffing equation.

Demonstrates effectiveness of the combined method for oscillatory nonlinear problems.

Provides a new tool for solving complex nonlinear differential equations.

Abstract

We present a method for the resolution of (oscillatory) nonlinear problems. It is based on the application of the Linear Delta Expansion to the Lindstedt-Poincar\'e method. By applying it to the Duffing equation, we show that our method substantially improves the approximation given by the simple Lindstedt-Poincar\'e method.