NUMERICAL APPROXIMATIONS OF FOURTH-ORDER PDES USING BLOCK UNIFICATION METHOD
AbstractIn this paper, a continuous linear multistep method is derived and used to formulate a block unification method (BUM), which is applied to solve fourth-order PDEs with appropriate initial and boundary conditions. Specifically, the method is used to solve the fourth order PDEs by first converting the PDEs into system of fourth-order ordinary differential equations (ODEs) via the method of lines, by replacing one of the variables with a finite difference method. The convergence properties of the method is discussed and some test problems are presented to demonstrate the accuracy of the method.
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