Five-diagonal sixth-order methods for two-point boundary value problems involving fourth-order differential equations

Abstract

We present a sixth order finite difference method for the two-point boundary value problem y ( 4 ) + f ( x , y ) = 0 {y^{(4)}} + f(x,y) = 0 , y ( a ) = A 0 y(a) = {A_0} , y ( b ) = B 0 y(b) = {B_0} , y ′ ( a ) = A 1 y\prime (a) = {A_1} , y ′ ( b ) = B 1 y\prime (b) = {B_1} . In the case of linear differential equations, our difference scheme leads to five-diagonal linear systems.