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A Meshfree Quasi-Interpolation Method for Solving Burgers’ Equation

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  • Mingzhu Li
  • Lijuan Chen
  • Qiang Ma

Abstract

The main aim of this work is to consider a meshfree algorithm for solving Burgers’ equation with the quartic B-spline quasi-interpolation. Quasi-interpolation is very useful in the study of approximation theory and its applications, since it can yield solutions directly without the need to solve any linear system of equations and overcome the ill-conditioning problem resulting from using the B-spline as a global interpolant. The numerical scheme is presented, by using the derivative of the quasi-interpolation to approximate the spatial derivative of the dependent variable and a low order forward difference to approximate the time derivative of the dependent variable. Compared to other numerical methods, the main advantages of our scheme are higher accuracy and lower computational complexity. Meanwhile, the algorithm is very simple and easy to implement and the numerical experiments show that it is feasible and valid.

Suggested Citation

  • Mingzhu Li & Lijuan Chen & Qiang Ma, 2014. "A Meshfree Quasi-Interpolation Method for Solving Burgers’ Equation," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-8, July.
    • Handle: RePEc:hin:jnlmpe:492072
    DOI: 10.1155/2014/492072
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    Cited by:

    1. Jiwari, Ram, 2022. "Local radial basis function-finite difference based algorithms for singularly perturbed Burgers’ model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 198(C), pages 106-126.

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