Where Does Smoothness Count the Most for Two-Point Boundary-Value Problems?

Where Does Smoothness Count the Most for Two-Point Boundary-Value Problems?

We are concerned with the complexity of 2mth order elliptic two-point boundary-value problems Lu = f. Previous work on the complexity of these problems has generally assumed that we had partial information about the right-hand side f and complete information about the coeecients of L, often making unrealistic assumptions about the smoothness of the coeecients of L. In this paper, we study probl...

B-SPLINE METHOD FOR TWO-POINT BOUNDARY VALUE PROBLEMS

In this work the collocation method based on quartic B-spline is developed and applied to two-point boundary value problem in ordinary diferential equations. The error analysis and convergence of presented method is discussed. The method illustrated by two test examples which verify that the presented method is applicable and considerable accurate.

Where does smoothness count the most for Fredholm equations of the second kind with noisy information?

We study the complexity of Fredholm problems (I − Tk)u = f of the second kind on the I d = [0, 1] , where Tk is an integral operator with kernel k. Previous work on the complexity of this problem has assumed either that we had complete information about k or that k and f had the same smoothness. In addition, most of this work has assumed that the information about k and f was exact. In this pap...

Approximating Initial-Value Problems with Two-Point Boundary-Value Problems: BBM-Equation

b-spline method for two-point boundary value problems

in this work the collocation method based on quartic b-spline is developed and applied to two-point boundary value problem in ordinary diferential equations. the error analysis and convergence of presented method is discussed. the method illustrated by two test examples which verify that the presented method is applicable and considerable accurate.