Exact three-point difference scheme for a nonlinear boundary-value problem on the semiaxis
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For the numerical solution of boundary-value problems on the semiaxis for second-order nonlinear ordinary differential equations, an exact three-point difference scheme is constructed and substantiated. Under the conditions of existence and uniqueness of solution of a boundary-value problem, we prove the existence and uniqueness of solution of the exact three-point difference scheme and convergence of the method of successive approximations for its solution.
KeywordsDifference Scheme Successive Approximation Contracting Mapping Nonlinear Ordinary Differential Equation Nonlinear Boundary Condition
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