Using a numerical method by omitting discretization of data to study numerical solutions for boundary value problems of fractional order differential equations
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DOI: 10.1002/mma.5800
Abstract: This manuscript is concerned to the numerical solutions by using shifted Jacobi polynomials (SJPs). By means of these polynomials, we construct some operational matrices (OMs) of fractional order integration and differentiation omitting collocations or discretization… read more here.
Keywords: order; numerical solutions; fractional order; numerical method ... See more keywords
An efficient numerical method for nonlinear fractional differential equations based on the generalized Mittag‐Leffler functions and Lagrange polynomials
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DOI: 10.1002/mma.6852
Abstract: In this paper, an efficient numerical method is developed for solving a class of nonlinear fractional differential equations. The main idea is to transform the nonlinear fractional differential equations into a system of integral equations… read more here.
Keywords: nonlinear fractional; numerical method; method; fractional differential ... See more keywords
A Numerical Method for Fracture Crossing Based on Average Stress Levels
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DOI: 10.1007/s00603-020-02054-x
Abstract: Due to the complexity of the interaction between hydraulic fractures (HFs) and natural fractures (NFs), several different interaction behaviours (arrest/cross/offset) may occur, according to hydraulic fracturing experiments. The existing analytical criteria cannot accurately describe this… read more here.
Keywords: numerical method; method fracture; method; stress ... See more keywords
A new numerical method for singularly perturbed turning point problems with two boundary layers based on reproducing kernel method
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DOI: 10.1007/s10092-016-0196-x
Abstract: In this paper, a simple numerical method is proposed for solving singularly perturbed boundary layers problems exhibiting twin boundary layers. The method avoids the choice of fitted meshes. Firstly the original problem is transformed into… read more here.
Keywords: numerical method; singularly perturbed; reproducing kernel; boundary layers ... See more keywords
A numerical method for solving the time fractional Schrödinger equation
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DOI: 10.1007/s10444-017-9579-z
Abstract: In this article, we proposed a new numerical method to obtain the approximation solution for the time-fractional Schrödinger equation based on reproducing kernel theory and collocation method. In order to overcome the weak singularity of… read more here.
Keywords: numerical method; fractional schr; time fractional; method ... See more keywords
A Numerical Method for a System of Integral Equations Determining the Boundaries of Local Nonhomogeneities
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DOI: 10.1007/s10598-020-09471-1
Abstract: The article considers a numerical method for the inverse problem of determining the boundaries of nonhomogeneities from probe data. A nonlinear system of integral equations in a three-dimensional region is solved and numerical results are… read more here.
Keywords: numerical method; determining boundaries; integral equations; system integral ... See more keywords
A Numerical Method for the Solution of Two Inverse Problems in the Mathematical Model of Redox Sorption
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DOI: 10.1007/s10598-020-09478-8
Abstract: For a mathematical model with internal-diffusion kinetics and an oxidation-reduction reaction, we consider two inverse problems of determining the sorption isotherm or the redox reaction rate constant from the output dynamic curve. A numerical method… read more here.
Keywords: numerical method; method solution; inverse problems; inverse ... See more keywords
An efficient numerical method for quasi-static crack propagation in heterogeneous media
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DOI: 10.1007/s10704-018-0284-9
Abstract: The paper is devoted to the problem of slow crack growth in heterogeneous media. The crack is subjected to arbitrary pressure distribution on the crack surface. The problem relates to construction of the so-called equilibrium… read more here.
Keywords: numerical method; quasi static; method quasi; efficient numerical ... See more keywords
An Efficient and Accurate Numerical Method for the Spectral Fractional Laplacian Equation
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DOI: 10.1007/s10915-019-01122-x
Abstract: We propose in this paper an efficient and accurate numerical method for the spectral fractional Laplacian equation using the Caffarelli–Silvestre extension. In particular, we propose several strategies to deal with the singularity and the additional… read more here.
Keywords: numerical method; accurate numerical; spectral fractional; method ... See more keywords
Novel numerical method of the fractional cable equation
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DOI: 10.1007/s12190-019-01302-w
Abstract: In this article, mainly based on the second order compact approximation of first order derivative, the novel numerical method with second order temporal accuracy and fourth order spatial accuracy is proposed to solve the fractional… read more here.
Keywords: numerical method; order; cable equation; fractional cable ... See more keywords
High-order efficient numerical method for solving a generalized fractional Oldroyd-B fluid model
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DOI: 10.1007/s12190-020-01458-w
Abstract: This paper investigates the high-order efficient numerical method with the corresponding stability and convergence analysis for the generalized fractional Oldroyd-B fluid model. Firstly, a high-order compact finite difference scheme is derived with accuracy $$O\left( \tau… read more here.
Keywords: numerical method; oldroyd fluid; high order; order ... See more keywords