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Solving nonlinear systems of fractional-order partial differential equations using an optimization technique based on generalized polynomials
Computational and Applied Mathematics ( IF 2.998 ) Pub Date : 2020-10-23 , DOI: 10.1007/s40314-020-01362-w
H. Hassani , J. A. Tenreiro Machado , E. Naraghirad , B. Sadeghi

This paper addresses the application of generalized polynomials for solving nonlinear systems of fractional-order partial differential equations with initial conditions. First, the solutions are expanded by means of generalized polynomials through an operational matrix. The unknown free coefficients and control parameters of the expansion with generalized polynomials are evaluated by means of an optimization process relating the nonlinear systems of fractional-order partial differential equations with the initial conditions. Then, the Lagrange multipliers are adopted for converting the problem into a system of algebraic equations. The convergence of the proposed method is analyzed. Several prototype problems show the applicability of the algorithm. The approximations obtained by other techniques are also tested confirming the high accuracy and computational efficiency of the proposed approach.



中文翻译:

基于广义多项式的优化技术求解分数阶偏微分方程的非线性系统

本文讨论了广义多项式在求解具有初始条件的分数阶偏微分方程非线性系统中的应用。首先,通过广义多项式通过运算矩阵扩展解。通过将分数阶偏微分方程的非线性系统与初始条件相关联的优化过程,来评估具有广义多项式的展开的未知自由系数和控制参数。然后,采用拉格朗日乘子将问题转换为代数方程组。分析了该方法的收敛性。几个原型问题表明了该算法的适用性。

更新日期:2020-10-30
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