Abstract
We present two new finite difference 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)=A 0, y′(a)=A 1, y(b)=B 0,y′(b)=B 1 . 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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