The FD-method for solving nonlinear Klein-Gordon equation
Volodymyr Makarov, Denis Dragunov, Dmytro Sember
TL;DR
This paper introduces a functional-discrete method for solving the nonlinear Klein-Gordon equation's Goursat problem, demonstrating superexponential convergence under certain conditions and validating results with numerical examples.
Contribution
The paper develops a new functional-discrete method with proven superexponential convergence for the nonlinear Klein-Gordon equation.
Findings
Method converges superexponentially under specified conditions
Numerical results align well with theoretical predictions
Provides a reliable approach for solving the nonlinear Klein-Gordon equation
Abstract
In the paper we present a functional-discrete method for solving the Goursat problem for nonlinear Klein-Gordon equation. The sufficient conditions providing that the proposed method converges superexponentially are obtained. The results of numerical example presented in the paper are in good agreement with the theoretical conclusions.
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Taxonomy
TopicsNonlinear Waves and Solitons · Fractional Differential Equations Solutions · Numerical methods for differential equations