Abstract-Boundary conditions in an unbounded domain, i.e. boundary condition at infinity, pose a problem in general for the numerical solution methods. The aim of this study is to overcome this difficulty by using Padé approximation with the differential transform method (DTM) on a form of classical Blasius equation. The obtained results are compared with, for the first time, the ones obtained by using a modified form of Adomian decomposition method (ADM). Furthermore, in order to see the consistency of solutions, they are also compared with the ones obtained by using variational iteration method (VIM).

We consider two nonlinear El Nino Southern Oscillation (ENSO) model to obtain approximate solutions with differential transform method for the first time. Efficiency, accuracy and error rates of solutions are compared with analytic solution, variational iteration and adomian decomposition solutions on the given tables and figures.

Integral transformations have been used for a long time in the solution of differential equations either solely or combined with other methods. These transforms provide a great advantage in reaching solutions in an easy way by transforming many seemingly complex problems into a more understandable format. In this study, we used an integral transform, namely Kashuri Fundo transform, by blending with the homotopy perturbation method for the solution of non-linear fractional porous media equation and time-fractional heat transfer equation with cubic non-linearity.

Recently, it has become quite common to investigate the solutions ofproblems that have an important place in scientific fields by using integraltransforms. The most important reason for this is that this transform allows thesimplest and least number of calculations to be made while reaching the solutionsof the problems. In this study, we are looking for a solution to the decay problem,which has a very important place in fields such as economics, chemistry, zoology,biology and physics, by using the Kashuri Fundo transform, which is one of theintegral transforms. In order to reveal the ease of use of this transform in reachingthe solution, some numerical applications were examined. The results of thesenumerical applications reveal that the Kashuri Fundo transform is quite efficient inreaching the solution of the decay problem.

Differential equations are expressions that are frequently encountered in mathematical modeling of laws or problems in many different fields of science. It can find its place in many fields such as applied mathematics, physics, chemistry, finance, economics, engineering, etc. They make them more understandable and easier to interpret, by modeling laws or problems mathematically. Therefore, solutions of differential equations are very important. Many methods have been developed that can be used to reach solutions of differential equations. One of these methods is integral transforms. Studies have shown that the use of integral transforms in the solutions of differential equations is a very effective method to reach solutions. In this study, we are looking for a solution to damped and undamped simple harmonic oscillations modeled by linear ordinary differential equations by using Kashuri Fundo transform, which is one of the integral transforms. From the solutions, it can be concluded that the Kashuri Fundo transform is an effective method for reaching the solutions of ordinary differential equations.