Title: Numerical Solutions of Klein-Gordon Equations: Finite Difference Methods Incorporated with Arithmetic Mean Averanging of Functional Values
Publisher: LAP LAMBERT Academic Publishing
Publication Date: 2016
Language: English
ISBN 10: 3659811521
ISBN 13: 9783659811524
Binding: Soft cover
Condition: New

About this title

Synopsis

The Klein-Gordon equation is a hyperbolic partial differential equation which appears in various relativistic physics areas such as quantum field theory and quantum mechanics. Many numerical approaches have been suggested to approximate the analytical solutions of the Klein-Gordon equation. However, the arithmetic mean method has not been studied on the Klein-Gordon equation. In this study, the new schemes for approximating the solution of the Klein-Gordon equations by applying central finite difference formula in time and space (CTCS) incorporated with arithmetic mean averaging of functional values are proposed. Three-point and four-point arithmetic means are considered. The schemes are applied to a linear and a nonlinear inhomogeneous Klein-Gordon equations with initial conditions. The theoretical aspects of the numerical scheme such as stability, consistency and convergence for the Klein-Gordon equations are also considered and the stability of the proposed schemes is analysed by using von Neumann stability analysis and Miller Norm Lemma.

About the Author

Noraini Kasron, MSc. of Sciences in Applied Mathematics, studied Computational Mathematics in Numerical Analysis at Universiti Teknologi MARA (Shah Alam), Malaysia.Mohd Agos Salim Nasir, PhD. in Numerical Analysis. Senior Lecturer at Universiti Teknologi MARA (Shah Alam), Malaysia.

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