ISSN:
1573-2878
Schlagwort(e):
Two-point boundary-value problems
;
calculus of variations
;
numerical methods
;
differential equations
;
computing methods
Quelle:
Springer Online Journal Archives 1860-2000
Thema:
Mathematik
Notizen:
Abstract In the parameter variation method, a scalar parameterk, kε[0, 1], is introduced into the differential equations. The parameterk is inserted in such a way that, whenk=0, the solution of the boundary-value problem is known or readily calculated and, whenk=1, the problem is identical with the original problem. Thus, bydeforming the solution step-by-step throughk-space fromk=0 tok=1, the original problem may be solved. These solutions then provide good starting values for any convergent, iterative scheme such as the Newton-Raphson method. The method is applied to the solution of problems with various types of boundary-value specifications and is further extended to take account of situations arising in the solution of problems from variational calculus (e.g., total elapsed time not specified, optimum control not a simple function of the variables).
Materialart:
Digitale Medien
URL:
http://dx.doi.org/10.1007/BF00935537
Permalink
