Comment on the paper “A class of methods based on non-polynomial spline functions for the solution of a special fourth-order boundary-value problems with engineering applications”

Abstract

Comment on the paper “A class of methods based on non-polynomial spline functions for the solution of a special fourth-order boundary-value problems with engineering applications” in Applied Mathematics and Computation 174 (2006) 1169–1180. The paper considered a class of two-point boundary-value problems of the form (1) d 4 y d x 4 + f ( x ) y = g ( x ) , a ⩽ x ⩽ b , (2) y ( a ) = A 1 , y ( b ) = A 2 , y ′ ( a ) = B 1 , y ′ ( b ) = B 2 , where f( x) and g( x) are continuous on [ a, b], and A i and B i ( i = 1, 2) are finite real constants. Here we correct some mistake in derivation of non-polynomial spline, boundary formulas, truncation errors, convergence analysis and computational experiments.