Abstract
A finite difference technique for variable rectilinear meshes is developed for numerical solutions of harmonic, biharmonic and multi-harmonic boundary value problems. A successive operator scheme is used to formulate a biharmonic equation from a harmonic one. The details of the computational procedure are included for torsion and plate bending problems which are governed by harmonic and biharmonic equations, respectively. The numerical results obtained from the present technique are compared with analytic and generalized finite difference solutions of Tseng and Gu for problems having regular and curved boundaries. Computations are then conducted to evaluate the accuracy of the solutions with different mesh arrangements.
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