Abstract
We discuss the construction of finite difference schemes for the two-point nonlinear boundary value problem:y (2n)+f(x,y)=0,y (2j)(a)=A 2j ,y (2j)(b)=B 2j ,j=0(1)n−1,n≧2. In the case of linear differential equations, these finite difference schemes lead to (2n+1)-diagonal linear systems. We consider in detail methods of orders two, four and six for two-point boundary value problems involving a fourth order differential equation; convergence of these methods is established and illustrated by numerical examples.
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References
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R. A. UsmaniAn O(h 6)finite difference analogue for the solution of some differential equations occuring in plate-deflection theory, J. Inst. Maths. Applics. 20 (1977), 331–333.
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Chawla, M.M., Katti, C.P. Finite difference methods for two-point boundary value problems involving high order differential equations. BIT 19, 27–33 (1979). https://doi.org/10.1007/BF01931218
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DOI: https://doi.org/10.1007/BF01931218