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An Explicit Single-Step Nonlinear Numerical Method for First Order initial value problems (IVPs)

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Journal of Applied Mathematics and Physics 2020年第9期8卷 1729-1735页

作者： Omolara Fatimah Bakre Ashiribo Senapon Wusu Moses Adebowale Akanbi Department of Mathematics & Statistics Federal College of Education (Technical) Lagos Nigeria Department of Mathematics Lagos State University Lagos Nigeria

Interest in the construction of efficient methods for solving initial value problems that have some peculiar properties with it or its solution is recently gaining wide popularity. Based on the assumption that the solution is representable by nonlinear trigonometric expressions, this work presents an explicit single-step nonlinear method for solving first order initial value problems whose solution possesses singularity. The stability and convergence properties of the constructed scheme are also presented. Implementation of the new method on some standard test problems compared with those discussed in the literature proved its accuracy and efficiency.

关键词： Ordinary Differential Equations First Order initial value problems Nonlinear Singularities

The Existence of Solutions of initial value problems for Nonlinear Second Order Impulsive Integro-Differential Equations of Mixed Type in Banach Spaces

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Journal of Mathematical Research and Exposition 2008年第3期28卷 501-510页

作者： YU Wei Qin CHEN Fang Qi Department of Mathematics Nanjing University of Aeronautics and Astronautics Jiangsu 210016 China

By the use of MSnch fixed point theorem and a new comparison result, the solutions of initial value problems for nonlinear second order impulsive integro-differential equations of mixed type in Banach spaces are inves... 详细信息

关键词： Banach spaces impulsive integro-differential equations initial value problems measure of noncompactness cone.

On the Solvability of Implicit Functional Equations with Applications to Discontinuous Differential Equations

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Acta Mathematica Sinica,English Series 2006年第1期22卷 223-232页

作者： S. HEIKKILA Department of Mathematical Sciences University of Oulu Box 3000 FIN-90014 University of Oulu Finland

In this paper we shall study the solvability of discontinuous functional equations, and apply the so-obtained results to discontinuous implicit initial value problems in ordered Banach spaces. The proofs are based on fixed point results in ordered spaces proved recently by the author. A concrete example is solved to demonstrate the obtained results.

关键词： Functional equations initial value problems Implicit Discontinuous nonlinearities

Existence of Solutions to a Singular initial value Problem

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Acta Mathematica Sinica,English Series 2007年第10期23卷 1797-1806页

作者： R.P.AGARWAL P.S.KELEVEDJIEV Department of Mathematical Sciences Florida Institute of TechnologyMelbourneFlorida 32901USA Department of Mathematics Technical University of SlivenSlivenBulgaria

Under the sign assumptions we investigate the global existence of solutions of the initial value problem x＇ =f（t, x, x＇）, x（0） = A, where the scalar function f（t, x,p） may be singular at x = A.

关键词： initial value problems first order differential equations singularity existence global solutions

Discretized Multisplitting AOR Waveform Relaxation Algorithms for initial value Problem of Systems of ODEs

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Chinese Quarterly Journal of Mathematics 1997年第4期12卷 27-35,页

作者：谷同祥李文强 Department of

The multisplitting algorithm for solving large systems of ordinary differential equations on parallel computers was introduced by Jeltsch and Pohl in [1]. On fixed time intervals conver gence results could be derived if the subsystems are solving ***,in theis paper,we deal with an extension of the waveform relaxation algorithm by us ing multisplittin AOR method based on an overlapping block decomposition. We restricted our selves to equidistant timepoints and dealed with the case that an implicit integration method was used to solve the subsystems numerically in parallel. Then we have proved convergence of multi splitting AOR waveform relaxation algorithm on a fixed window containing a finite number of timepoints.

关键词： systems of ordinary differential equations initial value problems multisplitting algorithm AOR method waveform relaxation algorithm

Construction of Third-Order Diagonal Implicit Runge-Kutta Methods for Stiff problems

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Chinese Physics Letters 2009年第8期26卷 39-41页

作者： Osama Yusuf Ababneh Rokiah@Rozita Ahmad School of Mathematical Sciences UniversRi Kebangsa~n Malaysia 43600 UKM Bangi Selangor Malaysia

We presents a new third-order diagonally implicit Runge^Kutta integration formula for stiff initial value problems, designed to be A-stable methods. The stability of the methods is analyzed and numerical results are s... 详细信息

关键词： RUNGE-Kutta formulas NUMERICAL integration initial value problems MATHEMATICAL analysis NUMERICAL analysis