NUMERICAL-SOLUTION OF 2-POINT BOUNDARY-VALUE-PROBLEMS

被引:15
作者
QUARTAPELLE, L
REBAY, S
机构
[1] Istituto di Fisica, Politecnico di Milano, 20133 Milan, Piazza Leonardo da Vinci
关键词
D O I
10.1016/0021-9991(90)90104-9
中图分类号
TP39 [计算机的应用];
学科分类号
081203 ; 0835 ;
摘要
This paper presents an original formulation of two-point boundary value and eigenvalue problems expressed as a system of first-order equations. The fundamental difference between the new method and other methods based on a first-order approach is the introduction of conditions of an integral character to supplement the simultaneous set of first-order equations, which are hence never regarded as an initial value problem. The consideration of integral conditions leads to establish a class of linear multipoint schemes for the numerical solution of boundary value problems for ordinary differential equations. Furthermore, the global character of the integral conditions (nonlocality) combined with the block structure of the system of algebraic equations allow dealing with stiff problems by means of the classical procedure of iterative refinement introduced by Wilkinson. The properties of the numerical schemes are illustrated by the solution of linear and nonlinear problems and by the accurate and efficient determination of some eigensolutions of a difficult problem of hydrodynamic stability. The proposed method is conceptually simpler and numerically more convenient than existing initial value methods, while still retaining all the advantages of a formulation based on a first-order system. © 1990.
引用
收藏
页码:314 / 354
页数:41
相关论文
共 44 条
[12]   SPECTRAL ALGORITHMS FOR VECTOR ELLIPTIC-EQUATIONS IN A SPHERICAL GAP [J].
DENNIS, SCR ;
QUARTAPELLE, L .
JOURNAL OF COMPUTATIONAL PHYSICS, 1985, 61 (02) :218-241
[13]   CALCULATION OF STEADY FLOW PAST A SPHERE AT LOW AND MODERATE REYNOLDS NUMBERS [J].
DENNIS, SCR ;
WALKER, JDA .
JOURNAL OF FLUID MECHANICS, 1971, 48 (AUG27) :771-&
[14]  
DENNIS SCR, 1986, COMMUNICATION
[15]  
Fox L., 1980, Computational Techniques for Ordinary Differential Equations. Proceedings of a Conference, P175
[16]   SOME IMPROVEMENTS INTHE USE OF RELAXATION METHODS FOR THE SOLUTION OF ORDINARY AND PARTIAL DIFFERENTIAL EQUATIONS [J].
FOX, L .
PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL AND PHYSICAL SCIENCES, 1947, 190 (1020) :31-59
[17]  
Fox L., 1957, NUMERICAL SOLUTION 2
[18]   NUMERICAL-METHODS FOR THE 1ST BIHARMONIC EQUATION AND FOR THE 2-DIMENSIONAL STOKES PROBLEM [J].
GLOWINSKI, R ;
PIRONNEAU, O .
SIAM REVIEW, 1979, 21 (02) :167-212
[19]  
HENRICI P., 1962, DISCRETE VARIABLE ME
[20]  
Isaacson E., 1966, ANAL NUMERICAL METHO