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A fourth-order finite difference method for the general one-dimensional nonlinear biharmonic problems of first kind

✍ Scribed by R.K. Mohanty

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
126 KB
Volume
114
Category
Article
ISSN
0377-0427

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✦ Synopsis

We present two new ÿnite di erence methods of order two and four in a coupled manner for the general one-dimensional nonlinear biharmonic equation y IV = f(x; y; y ; y ; y ) subject to the boundary conditions y(a) = A0; y (a) = A1; y(b) = B0; y (b) = B1. In both cases, we use only three grid points and do not require to discretize the boundary conditions. First-order derivative of the solution is obtained as a by-product of the methods. The methods are successfully applied to the problems both in cartesian and polar coordinates. Numerical examples are given to illustrate the methods and their convergence.

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