A new calculation technique for the Laplace and Sumudu transforms by means of the variational iteration method
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The aim of this study is to calculate the well-known Laplace and Sumudu transforms of functions in a different way. For our purpose, we present a computational tool by applying the variational iteration method. The Laplace and Sumudu transforms of some of the basic functions are also given as illustrations to test the efficiency and reliability of the proposed computational method.
KeywordsLaplace transform Sumudu transform Variational iteration method Linear IVP
Mathematics Subject Classification00A69 34A25 44A10 65R10
The variational iteration method (VIM) is one of the powerful mathematical tools to solve various kinds of linear and nonlinear problems which was proposed by He [1, 2, 3]. Besides these, variational iteration method and its modifications are also used in many areas of mathematics and science as seen [4, 5, 6, 7] and many others. In recent times, Fatoorehchi et al.  have performed the differential transform method (DTM) to obtain Laplace transform of functions. Also, the applications of homotopy perturbation (HPM) and adomian decomposition (ADM) methods for calculating Laplace transform are seen in the literature [9, 10], respectively.
Computing the Laplace and Sumudu transforms via VIM
In this section, Laplace and Sumudu transforms of some of the frequently used functions, especially used in the applied sciences, are obtained to show the efficiency and accuracy of the proposed computational method.
For Laplace transform
Here erf(t) and erfc(t) are well-known error and complementary error functions, respectively.
For Sumudu transform
We applied the variational iteration method for computing of the Laplace and Sumudu transforms of functions by using a different way. Results clearly show that unlike the literature and also classical computation, our presented method provides a powerful and easy calculation and also does not require too long operations. It is obviously indicated that the Laplace and Sumudu transforms of many functions, which are not mentioned here, can be computed by the VIM easily.
- 5.Wazwaz, A.M.: The variational iteration method for solving linear and nonlinear ODEs and scientific models with variable coefficients. Central Eur. J. Eng. 4(1), 64–71 (2014)Google Scholar
- 12.Williams, J.: Laplace Transforms, Problem Solvers. George Allen and Unwin, Crows Nest (1973)Google Scholar
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