| A Finite Difference Scheme for Blow-Up Solutions of Nonlinear Wave Equations |
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| 作者姓名： | Chien-Hong |
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| 摘 要： | <正>We consider a finite difference scheme for a nonlinear wave equation,whose solutions may lose their smoothness in finite time,i.e.,blow up in finite time.In order to numerically reproduce blow-up solutions,we propose a rule for a time-stepping, which is a variant of what was successfully used in the case of nonlinear parabolic equations.A numerical blow-up time is defined and is proved to converge,under a certain hypothesis,to the real blow-up time as the grid size tends to zero.
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| 关 键 词： | Nonlinear Wave Equations Solutions Blow-Up finite difference scheme nonlinear wave equation finite time blow-up solutions In order used in defined grid case |
A Finite Difference Scheme for Blow-Up Solutions of Nonlinear Wave Equations |
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| Chien-Hong.A Finite Difference Scheme for Blow-Up Solutions of Nonlinear Wave Equations[J].Numerical Mathematics A Journal of Chinese Universities English Series,2010,3(4). |
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| Authors: | Chien-Hong Cho |
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| Abstract: | We consider a finite difference scheme for a nonlinear wave equation, whose solutions may lose their smoothness in finite time, i.e., blow up in finite time. In order to numerically reproduce blow-up solutions, we propose a rule for a time-stepping,which is a variant of what was successfully used in the case of nonlinear parabolic equations. A numerical blow-up time is defined and is proved to converge, under a certain hypothesis, to the real blow-up time as the grid size tends to zero. |
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| Keywords: | Finite difference method nonlinear wave equation blow-up |
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