B-spline quasi-interpolation based numerical methods for some Sobolev type equations

Abstract

a b s t r a c tIn this article, we intend to use quadratic and cubic B-spline quasi-interpolants to develop higher order numerical methods for some Sobolev type equations in one space dimension. Our aim is also to compare the performance of the proposed methods in terms of the accuracy and the rate of convergence. We also discuss another approach to the cubic B-spline quasi-interpolation based method, where we achieve fourth order of accuracy in space. We theoretically establish the order of accuracy for the three proposed methods and also establish the L 2 -stability in the linear case using von Neumann analysis. As a particular case of the Sobolev type equations, we take the equal width and the Benjamin-Bona-Mahony-Burgers equations, and perform several numerical experiments to support our theoretical results.

Some Comparison of Solutions by Different Numerical Techniques on Mathematical Biology Problem

“…Recently, different scientists use the numerical method in their different problems. Here we try to give some references 2 International Journal of Differential Equations showing the importance of quasi-numerical methods techniques in present time: Kumar and Baskar [5] consider Bspline quasi-interpolation based numerical methods for some Sobolev type equations. Analytical and numerical study of dirty bosons in a quasi-one-dimensional harmonic trap is discussed by Khellil et al [6].…”

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A cubic B-spline quasi-interpolation method for solving two-dimensional unsteady advection diffusion equations

“…In this order, Zhu and Kang (2010a, 2010b) solved hyperbolic conservation laws using the quasi-interpolation based method. Kumar and Baskar (2016) developed higher order numerical schemes for particular one dimensional Sobolev type equations by implementing quadratic and cubic B-spline technique for quasi-interpolation. The authors also compared the performance of the proposed algorithm in terms of accuracy and the rate of convergence.…”

Solving Linear Optimal Control Problems Using Cubic B-spline Quasi-interpolation

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