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A new approach to nonlinear partial differential equations. (English) Zbl 0554.60065
The decomposition method [see the author, Stochastic systems (1983; Zbl 0523.60056)] has been significantly extended to cover the case of partial differential equations which may be nonlinear and/or stochastic. An important feature of the methodology is that no linearization or assumptions of ”weak nonlinearity” are involved and solutions are obtained in a computable manner without customary restrictive assumptions or discretization methods. (The method is discussed also in ”Stochastic systems II” expected to appear in early 1986.)

MSC:
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
35R60 PDEs with randomness, stochastic partial differential equations
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
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[1] Adomian, G, Stochastic systems, (1983), Academic Press New York · Zbl 0504.60066
[2] Adomian, G, On product nonlinearities in stochastic differential equations, Appl. math. comput., 8, 79-82, (1981) · Zbl 0454.60060
[3] Adomian, G; Bellman, R.E, On the Itô equation, J. math. anal. appl., 86, 2, 476-478, (1982) · Zbl 0484.60054
[4] Adomian, G; Malakian, K, Inversion of stochastic partial differential operators—the linear case, J. math. anal. appl., 77, 2, 505-512, (1980) · Zbl 0447.60045
[5] Adomian, G; Rach, R, Inversion of nonlinear stochastic operators, J. math. anal. appl., 91, 1, 39-46, (1983) · Zbl 0504.60066
[6] {\scG. Adomian and R. E. Bellman}, “New Methods for Partial Differential Equations,” Reidel, Dordrecht, in press. · Zbl 0557.35003
[7] {\scG. Adomian}, “Stochastic Systems II,” in press. · Zbl 0523.60056
[8] {\scG. Adomian}, “Applications of Stochastic Systems Theory to Physics and Engineering,” Academic Press, New York, in press. · Zbl 0659.93003
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