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A predictor-corrector scheme for the sine-Gordon equation. (English) Zbl 0951.65089
The authors consider an initial-boundary value problem involving a second-order nonlinear hyperbolic partial differential equation, known as sine-Gordon equation.
With reference to the numerical solution for this problem the authors use the method of lines approach to obtain an approximating system of second-order ordinary differential equations, use Padé approximants for the recurrence relation satisfied by the solution of this approximating system and design a predictor-corrector algorithm. They apply their algorithm to a test equation to do a stability analysis and use their numerical results to demonstrate the efficiency and accuracy of the predictor-corrector method over some earlier methods.
Reviewer: V.P.Tyagi (Bombay)

MSC:
65M20 Method of lines for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65L20 Stability and convergence of numerical methods for ordinary differential equations
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
35Q53 KdV equations (Korteweg-de Vries equations)
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