Abel-Gontscharoff boundary value problems

Mathl. Cornput. Modelling Vol. 17, No. 7, pp. 37-55, 1993 Printed in Great Britain

ABEL-GONTSCHAROFF

0895-7177193 $6.00 + 0.00 Pergamon Press Ltd

BOUNDARY

VALUE

PROBLEMS

RAVI P. AGARWAL AND QIN SHENG Department of Mathematics, National University of Singapore Kent Ridge, Singapore 0511 PATRICIA J. Y. WONG Division of Mathematics, Nanyang Technological University Bukit Timah Road, Singapore 1025

(Received May 1992; accepted June 1992) Abstract-In this paper, we shall provide necessary and sufficient conditions for the existence and uniqueness of solutions of general nth order nonlinear differential equations satisfying AbelGontscharoff boundary conditions. Sufficient conditions which guarantee the convergence of a general class of iterative methods are provided. Computational aspects of these iterative methods are also discussed. An example which dwells upon the importance of the obtained results is also included. 1. INTRODUCTION

In this paper,

we shall consider

the differential

y(n)= together

with the Abel-Gontscharoff

f(z, y, y’, . . . ,y+q

boundary

~%i+d

equation

=

conditions

-%+I,

U-1) [1,2]

O