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Multivalue Collocation Methods for Ordinary and Fractional Differential Equations [PDF]
Mathematics, 2022 The present paper illustrates some classes of multivalue methods for the numerical solution of ordinary and fractional differential equations. In particular, it focuses on two-step and mixed collocation methods, Nordsieck GLM collocation methods for ...
Angelamaria Cardone +3 more
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A New Approach for Solving Nonlinear Fractional Ordinary Differential Equations
Mathematics, 2023 Recently, researchers have been interested in studying fractional differential equations and their solutions due to the wide range of their applications in many scientific fields.
Hassan Kamil Jassim +1 more
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Fractional Calculus and Time-Fractional Differential Equations: Revisit and Construction of a Theory
Mathematics, 2022 For fractional derivatives and time-fractional differential equations, we construct a framework on the basis of operator theory in fractional Sobolev spaces.
Masahiro Yamamoto
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Mathematics, 2023 The analysis of differential equations using Lie symmetry has been proved a very robust tool. It is also a powerful technique for reducing the order and nonlinearity of differential equations.
Musrrat Ali +3 more
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Numerical methods for ordinary differential equations with applications to partial differential equations [PDF]
, 1983 This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.The thesis develops a number of algorithms for the numerical solution of ordinary differential equations with applications to partial differential equations.
Khaliq, Abdul Qayyum Masud
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On Euler methods for Caputo fractional differential equations [PDF]
, 2023 summary:Numerical methods for fractional differential equations have specific properties with respect to the ones for ordinary differential equations. The paper discusses Euler methods for Caputo differential equation initial value problem.
Tomášek, Petr
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Advances in Difference Equations, 2021 In this work, a technique for finding approximate solutions for ordinary fraction differential equations (OFDEs) of any order has been proposed. The method is a hybrid between Galerkin and collocation methods.
Mohamed Abdelhakem +3 more
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Similarity Solutions to Nonlinear Diffusion/Harry Dym Fractional Equations
Advances in Mathematical Physics, 2021 By using scalar similarity transformation, nonlinear model of time-fractional diffusion/Harry Dym equation is transformed to corresponding ordinary fractional differential equations, from which a travelling-wave similarity solution of time-fractional ...
Chao Yue +3 more
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Explicit and implicit methods for second order ordinary differential equations [PDF]
, 1980 A family of explicit formulas is developed for solving a system of second order linear ordinary differential equations with constant coefficients and with initial conditions specified.
Twizell, E H
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Searching closed form analytic solutions to some nonlinear fractional wave equations
Arab Journal of Basic and Applied Sciences, 2021 Numerous tangible incidents in physics, chemistry, applied mathematics and engineering are described successfully by means of models making use of the theory of derivatives of fractional order and research in this area has grown significantly.
Md. Tarikul Islam +2 more
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