Numerical solutions of the poisson equation

Abstract

In this article we shall give practical and numerical solutions of the Poisson equation on multidimensional spaces and show their numerical experiments by using computers.

Keywords:

• Poisson equation
• Inverse problem
• Approximation of functions
• Reproducing kernel
• Tikhonov regularization
• Sobolev space
• Generalized inverse
• Approximate inverse
• Error estimate
• Noise
• Weighted convolution inequality
• Mathematics Subject Classifications (2000): Primary 31A30
• 31B10
• 30C40
• 35A35

Acknowledgements

Saitoh wishes to express his deep thanks to Professor V.G. Romanov for his kind encouragement and suggestions on the paper [5]. Indeed, he, in particular, proposed error estimate problems in our inversion formulas in [5].

Notes

E-mail: [email protected]

E-mail: [email protected]

E-mail: [email protected]

Additional information

Notes on contributors

D.D. Trong ‡

E-mail: [email protected] E-mail: [email protected]