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”

摘要

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)d4ydx4+f(x)y=g(x),a⩽x⩽b,(2)y(a)=A1,y(b)=A2,y′(a)=B1,y′(b)=B2,where f(x) and g(x) are continuous on [a, b], and Ai and Bi (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.