#### Title

DISCRETIZATION PRINCIPLES FOR LINEAR TWO-POINT BOUNDARY VALUE PROBLEMS, III

#### Abbreviated Journal Title

Numer. Funct. Anal. Optim.

#### Keywords

Discretization principles; Finite difference methods; Two-point boundary; value problems; INVERSION; MATRICES; Mathematics, Applied

#### Abstract

This paper extends results of Yamamoto et al. (Numer. Funct. Anal. Optimiz. 2008; 29: 213-224) to the boundary value problem {-(p(x)u')' + q(x)u' + r (x) u = f(x), a <= x <= b, c(0)u(a) - c(1)u'(a) = d(0)u(b) + d(1)u'(b) = 0, where the sign of r(x) is indefinite. Let H(v)A(v)U(v) = f(v) be the finite difference equations on partitions Delta(v) : a = x(0)(v) < x(1)(v) < ... < x(nv+ 1)(v) = b, v = 1, 2,...with h(v) = max(i)(x(i)(v) - x(i-1)(v)) -> 0 as v -> infinity, where H(v) and A(v) are diagonal and tridiagonal matrices, respectively, and f(v) are vectors generated by discretization of f(x). Then equivalent conditions for the boundary value problem to have a unique solution u is an element of C(2)[a, b] are given in terms of H(v)(-1) and A(v)(-1).

#### Journal Title

Numerical Functional Analysis and Optimization

#### Volume

29

#### Issue/Number

9-10

#### Publication Date

1-1-2008

#### Document Type

Article

#### Language

English

#### First Page

1180

#### Last Page

1200

#### WOS Identifier

#### ISSN

0163-0563

#### Recommended Citation

"DISCRETIZATION PRINCIPLES FOR LINEAR TWO-POINT BOUNDARY VALUE PROBLEMS, III" (2008). *Faculty Bibliography 2000s*. 1154.

http://stars.library.ucf.edu/facultybib2000/1154

## Comments

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