A New Predictor-Corrector Method for Quasilinear First-Order Partial Differential Equations.

by J. L. Casti, H. H. Natsuyama, Robert E. Kalaba

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An effective, efficient method, exploiting the techniques of invariant imbedding and quasilinearization, for numerically solving quasilinear first-order partial differential equations. It is known that certain nonlinear two-point boundary-value problems can be converted into initial-value problems for a related quasilinear first-order partial differential equation. It is observed, conversely, that the treatment of the partial differential equation can be reduced to solving the two-point boundary-value problem by using quasilinearization. Use of standard finite difference methods to predict, and quasilinearization to correct, can yield precision solutions for the partial differential equation. 20 pp. Refs.

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