Solution of Nonlinear High Order Multi-Point Boundary Value Problems By Semi-Analytic Technique

In this paper, we present new algorithm for the solution of the nonlinear high order multi-point boundary value problem with suitable multi boundary conditions. The algorithm is based on the semi-analytic technique and the solutions are calculated in the form of a rapid convergent series. It is observed that the method gives more realistic series solution that converges very rapidly in physical problems. Illustrative examples are provided to demonstrate the efficiency and simplicity of the proposed method in solving this type of multi- point boundary value problems

On Spectral-Homotopy Perturbation Method Solution of Nonlinear Differential Equations in Bounded Domains

In this study, a combination of the hybrid Chebyshev spectral technique and the homotopy perturbation method is used to construct an iteration algorithm for solving nonlinear boundary value problems. Test problems are solved in order to demonstrate the efficiency, accuracy and reliability of the new technique and comparisons are made between the obtained results and exact solutions. The results demonstrate that the new spectral homotopy perturbation method is more efficient and converges faster than the standard homotopy analysis method. The methodology presented in the work is useful for solving the BVPs consisting of more than one differential equation in bounded domains.Â

Solution of Nonlinear High Order Multi-Point Boundary Value Problems By Semi-Analytic Technique

In this paper, we present new algorithm for the solution of the nonlinear high order multi-point boundary value problem with suitable multi boundary conditions. The algorithm is based on the semi-analytic technique and the solutions are calculated in the form of a rapid convergent series. It is observed that the method gives more realistic series solution that converges very rapidly in physical problems. Illustrative examples are provided to demonstrate the efficiency and simplicity of the proposed method in solving this type of multi- point boundary value problems

Розпаралелювання різницевих схем на основі ДС-алгоритму

Запропоновано новий алгоритм розпаралелювання у чисельному моделюванні. Він базується на методі розщеплення за просторовими змінними та ДС-алгоритмі і є ефективним при моделюванні фізичних процесів, що описуються початково-крайовими задачами для систем лінійних і нелінійних параболічних рівнянь другого порядку при виконанні закону збереження. Алгоритм дозволяє уникнути процедури розв'язування систем алгебраїчних різницевих рівнянь високого порядку. Доведено сумарну апроксимацію поставленої задачі та безумовну стійкість алгоритму.We propose a new algorithm of parallelization of a numerical modeling. It is based on the method of splitting a spatial variable and the DS-algorithm and is effective at the modeling of physical processes which are described by the initial-boundary-value problems for systems of linear and nonlinear parabolic equations of the second order with a law of conservation. The algorithm allows one to avoid the procedure of solving the systems of algebraic difference equations of higher order. The overall approximation of the task and the unconditional stability of the algorithm are proved