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Initial-value problems in potential theory. (English) Zbl 0241.65061


MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
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References:

[1] Bellman, R., Kagiwada, H., andKalaba, R.,Invariant Imbedding and the Numerical Integration of Boundary-Value Problems for Unstable Linear Systems of Ordinary Differential Equations, Communications of the Association for Computing Machinery, Vol. 10, No. 2, 1967. · Zbl 0148.39205
[2] Angel, E., andKalaba, R.,A One Sweep Numerical Method for Vector-Matrix Difference Equations with Two-Point Boundary Conditions, Journal of Optimization Theory and Applications, Vol. 6, No. 5, 1970. · Zbl 0193.12801
[3] Kagiwada, H., Kalaba, R., andSchumitzky, A.,An Initial-Value Method for Fredholm Equations, Journal of Mathematical Analysis and Applications, Vol. 19, No. 1, 1967. · Zbl 0264.65078
[4] Bellman, R., andOsborn, H. Dynamic Programming and the Variation of Green’s Functions, Journal of Mathematics and Mechanics, Vol. 7, No. 1, 1958. · Zbl 0083.12402
[5] Bergman, S., andSchiffer, M.,Kernal Functions and Elliptic Differential Equations in Mathematical Physics, Academic Press, New York, 1953.
[6] Angel, E.,Dynamic Programming and Linear Partial Differential Equations, Journal of Mathematical Analysis and Applications, Vol. 23, No. 3, 1968. · Zbl 0177.43701
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