| PERTURBATION SOLUTION OF THE WEAK-NONLINEAR DIFFERENTIAL EQUATION WITH δ-FUNCTION |
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| 引用本文： | 刘曾荣,魏锡荣. PERTURBATION SOLUTION OF THE WEAK-NONLINEAR DIFFERENTIAL EQUATION WITH δ-FUNCTION[J]. 应用数学和力学(英文版), 1984, 5(5): 1659-1665 |
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| 作者姓名： | 刘曾荣 魏锡荣 |
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| 摘 要： | In this paper, starting from some fundamental properties of Heaviside function and δ-function, making use of singular perturbation methods we provide a method of finding the asymptotic analytic solution of equation where M is an n -order linear differential operator, f(u) is a polynomial. By means of this method, we discuss some examples concretely. The results can be explained satisfac-torily in physics. If we deal with linear problem by this method, the result will agree with that drawn from theorem of impulse.
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| 收稿时间： | 1983-01-14 |
PERTURBATION SOLUTION OF THE WEAK-NONLINEAR DIFFERENTIAL EQUATION WITH δ-FUNCTION |
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| Liu Zheng-rong,Wei Si-rong. PERTURBATION SOLUTION OF THE WEAK-NONLINEAR DIFFERENTIAL EQUATION WITH δ-FUNCTION[J]. Applied Mathematics and Mechanics(English Edition), 1984, 5(5): 1659-1665 |
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| Authors: | Liu Zheng-rong Wei Si-rong |
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| Affiliation: | Anhui University, Heifei |
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| Abstract: | In this paper,starting from some fundamental properties of Heaviside function and δ -function,making use of singular perturbation methods we provide a method of finding the asymptotic analytic solution of equationwhere M(u)=eƒ+λ#948;(t-a) is an n -order linear differential operator,ƒ(u) is a polynomial. By means of this method,we discuss some examples concretely. The results can be explained satisfactorily in physics. If we deal with linear problem by this method,the result will agree with that drawn from theorem of impulse. |
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