New Approach for Numerical Solution of Poisson’s Equation by Cubic Spline

M. Yousefi^1, , J. Rashidinia¹, M. Yousefi², N.S BahrololoumiMofrad² and Mehdi Moudi³

¹School of Mathematics, Iran University of Science & Technology, Narmak, Tehran 16844-13114, Iran

²Energy and Mechanical Engineering Department, Abbaspour- power and water-College of Engineering, ShahidBeheshti University, P.O. Box.16765-1719, Tehran, Iran

³Institute of Applied Materials - Reliability of Components and Systems (IAM-ZBS) Engelbert-Arnold-Straße Karlsruhe, Germany

Cite this paper:
M. Yousefi, J. Rashidinia, M. Yousefi, N.S BahrololoumiMofrad and Mehdi Moudi. New Approach for Numerical Solution of Poisson’s Equation by Cubic Spline. Journal of Mathematical Sciences and Applications. 2014; 2(3):39-42. doi: 10.12691/jmsa-2-3-3

Abstract

We consider the solution of various boundary value problems for Poisson’s equation in the unit square using a nodal cubic spline collocation method and modifications of it which produce optimal fourth order approximations. Uniform partition of the square with cost O(N²log N) using a direct fast Fourier transform method. The numerical results exhibit super convergence phenomena.

Keywords:
Nodal collocation Poisson’s equation cubic spline convergence analysis

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