A new approach to boundary value equations and application to a generalization of Airy's equation

DOI10.1016/0022-247X(89)90083-8zbMath0678.65057MaRDI QIDQ1124296

M. Elrod, G. Adomian, Randolph C. Rach

Publication date: 1989

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

zbMATH Keywords

iterationexplicit solutionpower series solutionAiry's equation

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Applications to the sciences (65Z05) Special ordinary differential equations (Mathieu, Hill, Bessel, etc.) (34B30)

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Solution of boundary value problems by approaching spline techniques, Positive solutions of nonlinear fractional boundary value problems using Adomian decomposition method, Analytic solutions for nonlinear equations, On the solution of partial differential equations with specified boundary conditions, Convergence of Adomian's Method and Applications to Non‐linear Partial Differential Equations, A mathematical model of Adomian polynomials, Homotopy perturbation method to obtain positive solutions of nonlinear boundary value problems of fractional order, Solving differential equations using modified Picard iteration, A reliable algorithm for obtaining positive solutions for nonlinear boundary value problems, Variational iteration method for solving two-point boundary value problems, Appling Laplace Adomian decomposition method for delay differential equations with boundary value problems, A new definition of the Adomian polynomials, Numerical study of Fisher's equation by Adomian's method

Cites Work

• On the solution of partial differential equations with specified boundary conditions
• Nonlinear equations with mixed derivatives
• Inversion of nonlinear stochastic operators
• Variational Methods for Approximating Solutions of $\nabla ^2 u(x) = f(x) + k(x)u(x)$ and Generalizations