جستجوی مقالات مرتبط با کلیدواژه
تکرار جستجوی کلیدواژه numerical algorithms در نشریات گروه علوم پایه
numerical algorithms
در نشریات گروه ریاضی
تکرار جستجوی کلیدواژه numerical algorithms در مقالات مجلات علمی
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In the current study, a one-step numerical algorithm is presented to solve strongly non-linear full fractional duffing equations. A new fractional-order operational matrix of integration via quasi-hat functions (QHFs) is introduced. Utilizing the operational matrices of QHFs, the main problem will be transformed into a number of univariate polynomial equations. Absolute errors of the results in approximations and convergence analysis are addressed. Ultimately, five examples are provided to illustrate the capabilities of this algorithm. The numerical results are illustrated in some Tables and Figures, for different values of the parameters $\alpha~ and~ \beta$.Keywords: Fractional Duffing differential equations, Numerical algorithms, Strongly nonlinear, Quasi-hat function, Fractional operational matrix
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Iranian Journal of Numerical Analysis and Optimization, Volume:13 Issue: 3, Summer 2023, PP 500 -531In the current study, a new numerical algorithm is presented to solve a class of nonlinear fractional integral-differential equations with weakly singular kernels. Cubic hat functions (CHFs) and their properties are introduced for the first time. A new fractional-order operational matrix of integration via CHFs is presented. Utilizing the operational matrices of CHFs, the main problem is transformed into a number of trivariate polynomial equations. Error analysis and the convergence of the proposed method are evaluated, and the convergence rate is addressed. Ultimately, three examples are provided to illustrate the precision and capabilities of this algorithm. The numerical results are presented in some tables and figures.Keywords: Fractional integral-differential equations, Numerical algorithms, Weakly singular kernels, Cubic hat functions, Fractional operational matrix
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In this paper, we apply the homotopy analysis method (HAM) for solving fuzzy linear systems and present the necessary and sufficient conditions for the convergence of series solution obtained via the HAM. Also, we present a new criterion for choosing a proper value of convergence-control parameter $hbar$ when the HAM is applied to linear system of equations. Comparisons are made between the results of the HAM and several well-known numerical algorithms such as Jacobi method (JM), Gauss-Seidel method (GSM), successive over relaxation method (SOR), Adomian decomposition method (ADM) and homotopy perturbation method (HPM).Keywords: Fuzzy linear system, Homotopy analysis method, Convergence, control parameter, Numerical algorithms
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