Transformasi Laplace Secara Numerik Menggunakan Interpolasi Hermite dan Spline

Abstract

Laplace transform is a from of integral transform which has many applications in numerous fields. This transform converts a function  of a real variable to a function  of a complex variable. Function  can be found by evaluating the given integral of transform’s definition. In some cases, evaluation of integral of  can be too complicated to perform analytically. Then numerical integration is a way out to solve the problems. This paper introduces a simple numerical method of Laplace transform employing composite Simpson rule. Numerical integrations are performed at   to construct sequence  as approximation of . Hermite and spline interpolation is the applied to  in order to produce  as the numerical Laplace transform of . The accuracy of the proposed method is revealed by calculating the distance between  and  using  norm. As the results, function  can provide a decent approximation of  for some test functions. In general, Hermite interpolation produces  which is closer to  compared to the result obtained by spline interpolation.