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A NUMERICAL SCHEME FOR NONLINEAR KLEIN-GORDON EQUATIONS
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1983
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Unknown Venue
Numerical AnalysisNonlinear Wave PropagationNonlinear EquationNonlinear Hyperbolic ProblemNumerical TreatmentKlein-gordon EquationNonlinear Wave EquationsNonlinear Klein-gordon EquationNumerical Method For Partial Differential Equation
The finite difference method is useful in mathematical physics for solving the nonlinear wave equations. The key problem involved is how to deal with the nonlinear term.In this paper, numerical scheme for nonlinear Klein-Gordon equation is developed and an error estimation is established with the technique of [2-5].Based on the theory of nonlinear scheme given by Stetter[7] and Guo Benyu[2-6], the stability of this scheme is obtained from the error estimation.If the solution of Klein-Gordon equation has smooth derivatives andthen such stability implies the convergence.