Abstract
A simple, pseudo-spectral (collocation type) method is used to study Bratu's 2-parameter equation. The equation represent an important class of problems in both science and engineering. Simple polynomials are used to represent the dependent variable. The trial functions satisfy all the completeness requirement and make use of the various inherent symmetries of the problem to significantly reduce the size of the problem. The resulting nonlinear set of algebraic equations is solved using a constant-arc type method. For the 1-parameter Bratu's equation, the present results are found to be in good agreement with the previous results. Although the results were obtained using a main-frame computer, the present method can easily be used on a micro-computer. Results are obtained for variation of the value of the dependent parameter at the origin for different values of the two parameters. The present algorithm is capable of successfully obtaining the various turning points in both λ-u(0, 0) curves as well as ε-u(0, 0) curves. A discussion of the future research work is also given.
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Communicated by S.N. Atluri, January 27, 1989
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Kapania, R.K. A pseudo-spectral solution of 2-parameter Bratu's equation. Computational Mechanics 6, 55–63 (1990). https://doi.org/10.1007/BF00373799
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DOI: https://doi.org/10.1007/BF00373799