Pade Approximation Technique for the Solution of Singularly´ Perturbed Boundary Value Problem

Abstract: In this paper, the Pade approximation method was´ derived using the Taylor series, the condition at infinity is applied to the corresponding Pade approximation to the obtained´ series solution. We derived the solution of linear singularly perturbed second-order boundary value problems by dividing the problem into an inner region problem and outer region problem; expressing the inner and outer solution as asymptotic expansion; equating various terms in the inner and outer expressions to determine the constants in these expression; and combining the inner and outer solutions in some fashion to obtain a uniformly valid solution. The analysis of the results is drawn where we compare our results with the exact solution and also with the results of other authors. Finally, we observed that our proposed method is the same as the exact solution and is more efficient compared with the i-th order method.

Pade approximation, Singularly perturbed problem, boundary value problems, asymptotic expansions,numerical analysis

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