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Differential transform method: A comprehensive review and analysis [PDF]
Iranian Journal of Numerical Analysis and Optimization, 2022 The complexity of solving differential equations in real-world applications motivates researchers to extend numerical methods. Among different numerical and semi-analytical methods for solving initial and boundary value problems, the differential ...
S.H. Hashemi Mehne
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Initial Value Problems of Semilinear Supdiffusion Equations
Mathematics, 2020 We consider the existence of a mild solution of supdiffusion equations and obtain some results under some growth and noncompactness conditions of nonlinearity without coefficient restriction; and some new results for Ulam-Hyers-Rassias stability are ...
Yabing Gao, Yongxiang Li
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Rational Approximation Method for Stiff Initial Value Problems
Mathematics, 2021 While purely numerical methods for solving ordinary differential equations (ODE), e.g., Runge–Kutta methods, are easy to implement, solvers that utilize analytical derivations of the right-hand side of the ODE, such as the Taylor series method ...
Artur Karimov +3 more
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On a SHOCKLEY-READ-HALL model for semiconductors [PDF]
Theoretical and Applied Mechanics, 2013 The Shockley-Read-Hall model was introduced in 1952 to describe the statistics of recombination of holes and electrons in semiconductors occurring through the mechanism of trapping and we consider initial-boundary value problems with initial ...
Knežević-Miljanović Julka
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On the Non-Local Boundary Value Problem from the Probabilistic Viewpoint
Mathematics, 2022 We provide a short introduction of new and well-known facts relating non-local operators and irregular domains. Cauchy problems and boundary value problems are considered in case non-local operators are involved.
Mirko D’Ovidio
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New Algorithms for Dealing with Fractional Initial Value Problems
Axioms, 2023 This work purposes to establish two small numerical modifications for the Fractional Euler method (FEM) and the Modified Fractional Euler Method (MFEM) to deal with fractional initial value problems.
Iqbal M. Batiha +4 more
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A new type of shooting method for nonlinear boundary value problems
Alexandria Engineering Journal, 2013 In this article we introduce a new type of iterative method for initial value problems (IVPs). We enhance this method by using shooting techniques and interpolation for the boundary value problems. Our method is more accurate and applicable than built in
Muhammad Ahsan, Sarah Farrukh
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A new procedure of initial boundary value problems using homotopy perturbation method
Journal of Kufa for Mathematics and Computer, 2013 In this paper, , a new procedure is applied to treatment of initial boundary value problems by mixed initial and boundary conditions together  to obtain a new initial solution at every iteration using homotopy perturbation method.
Abeer Majeed Jassim +2 more
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Embedded Exponentially-Fitted Explicit Runge-Kutta-Nyström Methods for Solving Periodic Problems
Computation, 2020 In this work, a pair of embedded explicit exponentially-fitted Runge–Kutta–Nyström methods is formulated for solving special second-order ordinary differential equations (ODEs) with periodic solutions.
Musa Ahmed Demba +3 more
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Adaptive Piecewise Poly-Sinc Methods for Ordinary Differential Equations
Algorithms, 2022 We propose a new method of adaptive piecewise approximation based on Sinc points for ordinary differential equations. The adaptive method is a piecewise collocation method which utilizes Poly-Sinc interpolation to reach a preset level of accuracy for the
Omar Khalil +3 more
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