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A combined method based on -spline and sinc methods for solving two-dimensional unsteady convection-diffusion problems

J. Rashidinia|A. BARATI
장전수학회 (Jangjeon Mathematical Society)|2016.01|Advanced Studies in Contemporary Mathematics|제26권 제1호|pp. 147-164

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키워드

Convergence analysisSinc-Galerkin methodB-spline collocation method
주제분류수학

초록

In this work we construct a numerical method to solve the time-dependent convection-diffusion problems in case two dimensional for which the diffusion term can be small. we apply B-spline collocation method in x-direction and then the obtained system of ordinary differential equations can be solved by the sinc-Galerkin method . It is well known that the sinc procedure for the ordinary differential equations converges to the solution at an exponential rate. The convergence analysis is discussed for the obtained system of ordinary differential equations, the obtained results show that the convergence rate is exponentially. For efficiency and accuracy the method, we validate the proposed method by several examples, numerical results are investigated and confirm that oscillations can be controlled by our algorithm.

Abstract

In this work we construct a numerical method to solve the time-dependent convection-diffusion problems in case two dimensional for which the diffusion term can be small. we apply B-spline collocation method in x-direction and then the obtained system of ordinary differential equations can be solved by the sinc-Galerkin method . It is well known that the sinc procedure for the ordinary differential equations converges to the solution at an exponential rate. The convergence analysis is discussed for the obtained system of ordinary differential equations, the obtained results show that the convergence rate is exponentially. For efficiency and accuracy the method, we validate the proposed method by several examples, numerical results are investigated and confirm that oscillations can be controlled by our algorithm.

참고문헌 (40)

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