论文信息 - Fast finite-difference solution of biharmonic problems

Fast finite-difference solution of biharmonic problems

Setting the Reynolds number equal to zero, in a method for solving the Navier-Stokes equations numerically, results in a fast numerical method for biharmonic problems. The equation is treated as a system of two second order equations and a simple smoothing process is essential for convergence. An application is made to a crack-type problem.

Donald Greenspan | D. Schultz | D. Greenspan | D. Schultz

[1] Seymour V. Parter,et al. On “two-line” iterative methods for the Laplace and biharmonic difference equations , 1959, Numerische Mathematik.

[2] R. T. Dames,et al. On an Alternating Direction Method for Solving the Plate Problem with Mixed Boundary Conditions , 1960, JACM.

[3] M. Williams,et al. On the Stress Distribution at the Base of a Stationary Crack , 1956 .

[4] D. Greenspan. Lectures on the Numerical Solution of Linear, Singular, and Nonlinear Differential Equations , 1968 .

[5] Donald Greenspan,et al. A Numerical Approach to Biharmonic Problems , 1967, Comput. J..

[6] John R. Whiteman,et al. Numerical Treatment of Biharmonic Boundary Value Problems with Re-Entrant Boundaries , 1970, Comput. J..

[7] Garry J. Tee,et al. A Novel Finite-Difference Approximation to the Biharmonic Operator , 1963, Comput. J..

[8] L. Kantorovich,et al. Approximate methods of higher analysis , 1960 .

[9] Julius Smith,et al. The Coupled Equation Approach to the Numerical Solution of the Biharmonic Equation by Finite Differences. II , 1968 .

[10] Numerical solution of the first biharmonic problem by linear programming , 1963 .

[11] Donald Greenspan,et al. Numerical Studies of Prototype Cavity Flow Problems , 1969, Comput. J..