作者：
Niu, XinJiang, ZhenghuaHefei Univ
Dept Math & Phys 99 Jinxiudadao Rd Hefei 230601 Anhui Peoples R China Nanjing Univ
Dept Math 22 Hankou Rd Nanjing 210093 Jiangsu Peoples R China
A set of sufficient conditions related to a class of initialvalueproblems are given for the global diffeomorphism of a nonlinear mapping F. In addition, the results obtained are used to discuss the existence and uni...
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A set of sufficient conditions related to a class of initialvalueproblems are given for the global diffeomorphism of a nonlinear mapping F. In addition, the results obtained are used to discuss the existence and uniqueness of solution for the boundary valueproblems.
Some methods for solving initialvalueproblem used to solve the boundary valueproblem (BVP) of ordinary differential equation were discussed and contrasted. These methods include the finite difference method, shooti...
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Some methods for solving initialvalueproblem used to solve the boundary valueproblem (BVP) of ordinary differential equation were discussed and contrasted. These methods include the finite difference method, shooting method, fixed-point method and numerical continuation method. The study results show that these methods are very effective to solve BVP. Especially, the fixed-point method and the continuation method can save computing time and memory element.
The present paper develops two iterative algorithms to determine the periods and then the periodic solutions of nonlinear jerk equations. We consider two possible cases: initialvalues unknown and initialvalues given...
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The present paper develops two iterative algorithms to determine the periods and then the periodic solutions of nonlinear jerk equations. We consider two possible cases: initialvalues unknown and initialvalues given. A shape function method is introduced, by which we can transform the periodic problem to an initialvalueproblem for the new variable, while the period and the terminal values of the new variable at the end of a period are determined iteratively. The initial value problem method (IVPM) can satisfy the periodic conditions exactly. Three examples reveal the advantages of the new iterative algorithms based on the IVPM, which converge fastly and also provide very accurate periodic solutions and periods of the nonlinear jerk equations. (C) 2019 Elsevier Ltd. All rights reserved.
We introduce a coordinate transformation of independent variable, such that the second-order nonlinear singularly perturbed boundary valueproblem (SPBVP) in the transformed coordinate is less stiff within the boundar...
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We introduce a coordinate transformation of independent variable, such that the second-order nonlinear singularly perturbed boundary valueproblem (SPBVP) in the transformed coordinate is less stiff within the boundary layer. An initialvalueproblem for a new dependent variable can be derived easily through the variable transformation. While the zero initialvalues are given, an unknown terminal value of the new variable at the right end is determined iteratively. We propose the modifications of the asymptotic solution and the uniform approximate solution of the SPBVP;hence, the modified analytic solutions can exactly satisfy both the boundary conditions at two ends. Some examples confirm that the novel methods can achieve better analytic and numerical solutions of the nonlinear SPBVP. (C) 2021 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.
For a second-order quasilinear singularly perturbed problem under the Dirichlet boundary conditions, we propose a new asymptotic numerical method, which involves two problems: a reduced problem with a one-side boundar...
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For a second-order quasilinear singularly perturbed problem under the Dirichlet boundary conditions, we propose a new asymptotic numerical method, which involves two problems: a reduced problem with a one-side boundary condition and a novel boundary layer correction problem with a two-sided boundary condition. Through the introduction of two new variables, both problems are transformed to a set of three first-order initialvalueproblems with zero initial conditions. The Runge-Kutta method is then applied to integrate the differential equations and to determine two unknown terminal values of the new variables until they converge. The modified asymptotic numerical solution satisfies the Dirichlet boundary conditions. Some examples confirm that the newly proposed method can achieve a better asymptotic solution to the quasilinear singularly perturbed problem. For most values of the perturbing parameter, the present method not only preserves the inherent asymptotic property within the boundary layer but also improves the accuracy within the entire domain.
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