Trial solution methods to solve unsteady PDE

Al‐Nimr, M. A.; Aljarrah, Majed; Al-Shyyab, Ahmad

doi:10.1016/0735-1933(94)90075-2

Cited by 2 publications

(1 citation statement)

References 8 publications

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“…Examples of these analytical and semi-analytical solving techniques were presented in Scott (2003), Arthur (1995) and Richard and Roth (1984). These techniques include separation of variables, integral transforms, method of characteristics, change of variables, fundamental solution, superposition principles, Laplace transformation technique, Fourier series and Fourier integral technique, similarity solution technique, trial solution methods (collocation, sub domain, least square and Galerkin methods), variation methods and combining trial solution methods with Laplace transformation, trial solutions were discussed by Al-Nimr et al (1994) and Kiwan et al (2000).…”

Section: Introductionmentioning

confidence: 99%

A Novel Hybrid Solving Approach Based on Combining Similarity Solutions with Laplace Transformation Technique to Solve Different Engineering Problems

Khuwaileh¹,

Al‐Nimr²,

Alata³

2014

RJASET

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In this study Laplace transformation technique combined with similarity solutions are used to solve PDE involves derivatives with respect to time and two spatial parameters. The hybrid approach is based on transforming the PDE from the real physical time domain to the Laplacian domain. The obtained PDE in the Laplacian domain involves only derivatives with respect to the two spatial parameters. This transformed PDE is then solved by similarity solution approach to convert it from a PDE in the Laplacian domain to an ODE in another domain involves independent parameter consists of the Laplace parameter s and the two independent spatial parameters. A case is discussed to demonstrate the capabilities of the proposed approach in solving different engineering problems.

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