Differential transformation method for solving sixth-order boundary value problems of ordinary differential equations

In this study, sixth-order boundary value problems for linear and nonlinear differential equations have been solved by using Differential Transformation Method (DTM). The numerical solutions are given in several examples. For each example, the solution given by DTM is compared with the exact solution. Absolute relative error (ARE) for each iteration can be computed. Therefore, the maximum absolute relative error (MARE) of the DTM can be obtained. To show that the solution given by the DTM has higher level of accuracy, the absolute relative error of the DTM has been compared with the other methods such as Adomian decomposition method with Green’s function, modified decomposition method (MDM), homotopy perturbation method (HPM), Variational Iteration Method (VIM) and Quintic B-Spline Collocation Method. Comparison graphs are given at the end of this paper. The obtained result shows that the proposed method is able to provide better approximation in term of accuracy

Differential Transformation Method for Solving Sixth-Order Boundary Value Problems of Ordinary Differential Equations

In this study, sixth-order boundary value problems for linear and nonlinear differential equations have been solved by using Differential Transformation Method (DTM). The numerical solutions are given in several examples. For each example, the solution given by DTM is compared with the exact solution. Absolute relative error (ARE) for each iteration can be computed. Therefore, the maximum absolute relative error (MARE) of the DTM can be obtained. To show that the solution given by the DTM has higher level of accuracy, the absolute relative error of the DTM has been compared with the other methods such as Adomian decomposition method with Green’s function, modified decomposition method (MDM), homotopy perturbation method (HPM), Variational Iteration Method (VIM) and Quintic B-Spline Collocation Method. Comparison graphs are given at the end of this paper. The obtained result shows that the proposed method is able to provide better approximation in term of accuracy

A one-way dissection of high-order compact scheme for the solution of 2D Poisson equation

We present a one-way dissection formulation of high-order compact scheme for the solution of 2D Poisson equation. One-way dissection is a type of matrix reordering, divide and conquers procedure. Efficient and concise compact schemes of 4th and 6th orders are derived using the truncation errors of the Taylors’ series expansion of the governing equation. The system is split into sub-domains and each sub-domain is treated separately. Two test problems are solved to show the fourth order performance of the scheme. The direct method is used to achieve a quick solution to the problems