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A differential-difference technique for the hybrid computer solution of parabolic partial differential equations

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  • Petrov, Andrey A.

Abstract

A differential-difference technique for the hybrid computer solution of parabolic partial differential equations with nonlinear terms is described. A theoretical analysis of the computational stability, convergence and accuracy of the technique is presented, showing that the method has certain important advantages over classical finite difference methods. The practical application of the technique to a biomedical problem is described as an example, confirming the efficiency of this approach.

Suggested Citation

  • Petrov, Andrey A., 1975. "A differential-difference technique for the hybrid computer solution of parabolic partial differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 17(2), pages 104-109.
    • Handle: RePEc:eee:matcom:v:17:y:1975:i:2:p:104-109
    DOI: 10.1016/S0378-4754(75)80021-8
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    Cited by:

    1. Lawson, P.A., 1981. "Contraction mapping techniques applied to the hybrid computer solution of parabolic PDE's," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 23(3), pages 299-303.
    2. Bakasov, A.A. & Yukalov, V.I., 1989. "Microscopic theory of spin reorientations- thermodynamics and nucleation phenomenon," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 162(1), pages 31-66.
    3. Neundorf, W. & Schoenefeld, Re., 1980. "Stable iterative hybrid method for the solution of weak nonlinear parabolic differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 22(1), pages 1-6.
    4. Bakasov, A.A. & Yukalov, V.I., 1989. "Microscopic theory of spin reorientations - heterophase approach and basic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 157(3), pages 1203-1226.

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