Abstract
The aim of this study is to apply a novel technique to control the accuracy and error of the Adomian decomposition method (ADM) for solving nonlinear shallow water wave equation. The ADM is among semi-analytical and powerful methods for solving many mathematical and engineering problems. We apply the Controle et Estimation Stochastique des Arrondis de Calculs (CESTAC) method which is based on stochastic arithmetic (SA). Also instead of applying mathematical packages we use the Control of Accuracy and Debugging for Numerical Applications (CADNA) library. In this library we will write all codes using C++ programming codes. Applying the method we can find the optimal numerical results, error and step of the ADM and they are the main novelties of this research. The numerical results show the accuracy and efficiency of the novel scheme.
Highlights
Bresch et al in [5] have focused on some compressible fluid models specially the shallow water system
In floating point arithmetic (FPA) in order to show the accuracy we should apply the traditional conditions which are based on the exact solution and as follows shows the informatical zero which can be produced only in stochastic arithmetic (SA) when we apply the CESTAC method and the CADNA library. It shows that number of common significant digits (NCSDs) of two successive iterations are almost zero
Applying the Adomian d ecomposition method (ADM) for solving the shallow water wave problem (1), the NCSDs of the exact and approximate solutions are almost equal to the NCSDs of two successive approximations as
Summary
Численная валидация метода разложения Адомиана для решения нелинейного уравнения мелкой воды. Целью данной работы является применение новой методики для проведения эффективного контроля точности и анализа погрешности применения метода разложения Адомиана для решения нелинейного волнового уравнения мелкой воды, возникающего при выполнении ряда важных задач в различных областях машиностроения и теории материалов. Н. Численная валидация метода разложения Адомиана для решения. Также вместо применения стандартных математических пакетов в работе эффективно использована библиотека контроля точности и отладки для численных приложений CADNA (Control of Accuracy and Debugging for Numerical Applications). Приведены результаты тестирования разработа нной численной модели для решения уравнения мелкой воды. При проведении численных расчетов с использованием предлагаемого метода разложения Адомиана продемонстрирована высокая точность и эффективность разработанного подхода для решения нелинейного волнового уравнения мелкой воды. Н. Численная валидация метода разложения Адомиана для решения нелинейного уравнения мелкой воды // iPolytech Journal.
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