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On the Numerical Inversion of the Laplace Transform by the Use of an Optimized Legendre Polynomial
Abdulaziz, Al-Shuaibi 한국산업정보응용수학회 2000 한국산업정보응용수학회 Vol.4 No.1
A method for inverting the Laplace transform is presented, using a finite series of the classical Legendre polynomials. The method recovers a real-valued function f (t) in a finite interval of the positive real axis when f (t) belongs to a certain class W_(β) and requires the knowledge of its Laplace transform F(s) only at a finite number of discrete points on the real axis s > 0. The choice of these points will be carefully considered so as to improve the approximation error as well as to minimize the number of steps needed in the evaluations. The method is tested on few examples, with particular emphasis on the estimation of the error bounds involved.