The solutions of many advanced engineering problems like Fick"s second law, heat and mass transfer problems, vibrating beams problems contains error and complementary error function. When we use any integral transform to solve these types of problems, it is very necessary to know the integral transform of error function. In this article, we find the Mohand transform of error and complementary error functions. To demonstrate the usefulness of Mohand transform of error function, some numerical applications are considered in application section for solving improper integrals which contain error function. It is pointed out that Mohand transform give the exact solution of improper integral which contains error function without any tedious calculation work.
A plethora of higher order iterative methods, involving derivatives in algorithms, are available in the literature for finding multiple roots. Contrary to this fact, the higher order methods without derivatives in the iteration are difficult to construct, and hence, such methods are almost non-existent. This motivated us to explore a derivative-free iterative scheme with optimal fourth order convergence. The applicability of the new scheme is shown by testing on different functions, which illustrates the excellent convergence. Moreover, the comparison of the performance shows that the new technique is a good competitor to existing optimal fourth order Newton-like techniques.
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