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A Tutorial to Approximately Invert the Sumudu Transform
Department of Biomedical Engineering, Stevens Institute of Technology, Hoboken, NJ, USA
Department of Biomedical Engineering, Rutgers University, Piscataway, NJ, USA
Department of Anesthesiology, Rutgers New Jersey Medical School, Newark, NJ, USA
- 1 Department of Biomedical Engineering, Stevens Institute of Technology, Hoboken, NJ, USA
- 2 Department of Biomedical Engineering, Rutgers University, Piscataway, NJ, USA
- 3 Department of Anesthesiology, Rutgers New Jersey Medical School, Newark, NJ, USA
Applied Mathematics·Volume 10 (2019)·Pages 1004–1028·Published 24 October 2019·DOI10.4236/am.2019.1011070
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Abstract
Unlike the traditional Laplace transform, the Sumudu transform of a function, when approximated as a power series, may be readily inverted using factorial-based coefficient diminution. This technique offers straightforward computational advantages for approximate range-limited numerical solutions of certain ordinary, mixed, and partial linear differential and integro-differential equations. Furthermore, discrete convolution (the Cauchy product), may also be utilized to assist in this approximate inversion method of the Sumudu transform. Illustrative examples are provided which elucidate both the applicability and limitations of this method.
KeywordsSumudu TransformDouble SeriesDiscrete ConvolutionCauchy Product
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