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Runge-Kutta Numerical Methods and Applications to Differential Equation Models

Author: QinJun
Tutor: WangLiangLong
School: Anhui University
Course: Basic mathematics
Keywords: Differential Equations Runge-Kutta method Numerical Solution Two species coexistence model Economic dynamics model Epidemic Model
CLC: O241.8
Type: Master's thesis
Year: 2010
Downloads: 303
Quote: 0
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Abstract


Practical problems in the study , we often need to build mathematical models to solve. Establish ODE model is an effective means of dealing with such issues one . Unfortunately, the differential equation model is difficult or impossible to obtain the analytical solution . For this reason, often use their numerical solution Find the numerical solution of differential equations , while the Runge-Kutta method of numerical solution is an important method . This article discusses the numerical solution of the Runge-Kutta method , and gives a few simple applications . Main content is to use a standard fourth-order Runge-Kutta method for differential equations of the model established by numerical solution , and gives the iteration formula for solving , but also on the convergence of the judgment ; final differential equations using MATLAB programming model for the numerical simulation and make a graph. This paper has five main parts : the first part describes the background and significance of this topic . Then introduced the main contents of this article do . The second part describes the background Runge-Kutta , formulas derived , convergence judgment theorem , absolutely stable regional and local error . The third part through rational model assumes that established the two species coexist differential equation model , given the use of a standard fourth-order Runge-Kutta method for solving equations and numerical calculation , the final model to analyze research results of the two species each other changes due to the influence . The fourth section, under the assumption that we have the right to establish a dynamic model of the economy , given formula to solve this model , and using Matlab programming for numerical calculations , and finally an analysis of the model . Part V establishes a dynamic model of infectious diseases , given the standard fourth-order Runge-Kutta method to solve the format and using Matlab programming for numerical calculations , and finally make a theoretical study of the model , obtained the key factors affecting disease to help control the spread of disease .

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CLC: > Mathematical sciences and chemical > Mathematics > Computational Mathematics > Numerical Analysis > The numerical solution of differential equations, integral equations
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