Decomposition solution of nonlinear hyperbolic equations. (English) Zbl 0729.65072
The application of the decomposition method previously proposed by the author to dissipative wave equations of the form \(u_{tt}- u_{xx}+(\partial /\partial t)(f(u))=g\) is discussed. The initial- boundary value problem \(u_{tt}-u_{xx}+(\partial /\partial t)(u^ 2)=-2 \sin^ 2x\cdot \sin t\cdot \cos t,\) \(u(0,t)=u(\pi,t)=0,\) \(u(x,0)=\sin x,\) \(u_ t(x,0)=0\) is considered as an illustration.
Reviewer: S.E.Zhelezovsky (Saratov)
MSC:
| 65M55 | Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs |
| 35L70 | Second-order nonlinear hyperbolic equations |
References:
| [1] | Adomian, G., Nonlinear Stochastic Operator Equations (1986), Academic Press · Zbl 0614.35013 |
| [2] | Adomian, G., Applications of Nonlinear Stochastic Systems Theory and Applications to Physics (1988), Kluwer · Zbl 0666.60061 |
| [3] | Bellomo, N.; Riganti, R., Nonlinear Stochastic Systems in Physics and Mechanics (1987), World Scientific: World Scientific Singapore · Zbl 0623.60084 |
| [4] | Adomian, G., Stochastic Systems (1983), Academic Press · Zbl 0504.60066 |
| [5] | Cherruault, Y., Convergence of Adomian’s Method, Kybernetes, vol. 18, no. 2, 31-38 (1989) · Zbl 0697.65051 |
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