کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4627073 | 1631801 | 2015 | 10 صفحه PDF | دانلود رایگان |
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.
Journal: Applied Mathematics and Computation - Volume 253, 15 February 2015, Pages 377–386