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.)


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)


Zbl 0523.60056
Full Text: DOI


[1] Adomian, G., Stochastic Systems (1983), Academic Press: 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] G. Adomian and R. E. Bellman; G. Adomian and R. E. Bellman · Zbl 0557.35003
[7] G. Adomian; G. Adomian · Zbl 0523.60056
[8] G. Adomian; G. Adomian · Zbl 0659.93003
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