Solving time-dependent differential equations by multiquadric trigonometric quasi-interpolation

Wenwu Gao and Zongmin Wu

Applied Mathematics and Computation, 2015, vol. 253, issue C, 377-386

Abstract: Multiquadric (MQ) quasi-interpolation is a popular method for the numerical solution of differential equations. However, MQ quasi-interpolation is not well suited for the equations with periodic solutions. This is mainly due to the fact that its kernel (the MQ function) is not a periodic function. A reasonable way of overcoming the difficulty is to use a quasi-interpolant whose kernel itself is also periodic in these cases. The paper constructs such a quasi-interpolant. Error estimates of the quasi-interpolant are also provided. The quasi-interpolant possesses many fair properties of the MQ quasi-interpolant (i.e., simplicity, efficiency, stability, etc). Moreover, it is more suitable (than the MQ quasi-interpolant) for periodic problems since the quasi-interpolant as well as its derivatives are periodic. Examples of solving both linear and nonlinear partial differential equations (whose solutions are periodic) by the quasi-interpolant and the MQ quasi-interpolant are compared at the end of the paper. Numerical results show that the quasi-interpolant outperforms the MQ quasi-interpolant for periodic problems.

Keywords: Quasi-interpolation; Multiquadric trigonometric functions; Numerical solution of differential equations; Meshless methods; Divided differences (search for similar items in EconPapers)
Date: 2015
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:253:y:2015:i:c:p:377-386

DOI: 10.1016/j.amc.2014.12.008

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