On the solution of nonlinear differential equations with convolution product nonlinearities. (English) Zbl 0588.34004
Transform techniques can be used with differential equations containing convolution product nonlinearities to yield an algebraic equation for which the Adomian polynomials are more easily obtained for solution by the decomposition method.
MSC:
| 34A12 | Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations |
| 34A34 | Nonlinear ordinary differential equations and systems |
| 44A10 | Laplace transform |
Keywords:
first order differential equation; Transform techniques; convolution product nonlinearities; Adomian polynomialsReferences:
| [1] | Adomian, G., Stochastic Systems (1983), Academic Press: Academic Press New York · Zbl 0504.60066 |
| [2] | Adomian, G., Nonlinear Stochastic Operator Equations (1986), Academic Press: Academic Press New York · Zbl 0614.35013 |
| [3] | Rach, R., A convenient computational form for the Adomian polynomials, J. Math. Anal. Appl., 102, 415-419 (1984) · Zbl 0552.60061 |
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