New Approach to Compute Integral Transforms

Integral transforms find special applicability within scientific and mathematical disciplines. A powerful and efficient homotopy methodology in evaluating integrals arises in integral transforms was presented. The method depends on solving a related first order linear differential equation by homotopy analysis method HAM. The Laplace transform, Fourier transform and the moment generating function of the standard normal distribution were used as test examples to show the efficiency of the method. The results obtained justify the advantage of this methodology. MATLAB 7 was used to carry out the computations.