Numerical solution of second order one dimensional hyperbolic equation by exponential B-spline collocation method
Swarn Singh1, Suruchi Singh2, R. Arora3
1University of Delhi, New Delhi, 110021, India
2DM University of Delhi, New Delhi, 110007, India
3AM University of Delhi, Delhi, 110039, India
Keywords: уравнение затухающей волны, SSPRK(2,2), метод экспоненциальных В-сплайнов, телеграфное уравнение, трехдиагональный решатель, безусловно устойчивый метод, damped wave equation, exponential B-spline method, telegraphic equation, tri-diagonal solver, unconditionally stable method
Abstract
In this paper, we propose a method based on collocation of exponential B-splines to obtain numerical solution of nonlinear second order one dimensional hyperbolic equation subject to appropriate initial and Dirichlet boundary conditions. The method is a combination of B-spline collocation method in space and two stage, second order strong-stability-preserving Runge-Kutta method in time. The proposed method is shown to be unconditionally stable. The efficiency and accuracy of the method are successfully described by applying the method to a few test problems.
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