Numerical Solution of Laplace's and Poisson's Equations with Applications to Photoelasticity and Torsion, 101–110. numberCollege of Engineering, the Ohio State University, 1940 - 51 pages |
Contents
THE NUMERICAL SOLUTION OF LAPLACES EQUATION | 1 |
Theory | 5 |
Technique | 14 |
12 other sections not shown
Common terms and phrases
A₁ accuracy āij Appendix approximately arbitrary asymptotic value average axis of symmetry b₁ boundary points calculation coarse coefficients computed constant continuous solution corresponding cross section determined difference equation difference function differential equation discussion e₁ eigenvalue eigenvector equa error factor final solution four diagonal neighbors four nearest neighbors four neighbors four-block function values given hence improved values improvement formulas improvement process interior points interpolation intersects interval h itera iteration labor Laplace's equation lattice Liebmann procedure maximum nets nine-block procedure node number of traverses numerical methods numerical solution obtained Ohio State University order of improvement p² log photoelastic Poisson's equation principal stresses problem quadric rate of convergence ratio reduced region result satisfy scale-factor seventh-order shaft shear Shortley significant figures slope SOLUTION OF LAPLACE'S solving square tion torque volume torsion trial function true solution y-surface zero boundary values λ₁