ISSN:
0029-5981
Keywords:
Engineering
;
Engineering General
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Mathematics
,
Technology
Notes:
A numerical method is presented for the-solution of linear systems of differential equations with initial-value or two-point boundary conditions. For y′(x) = A(x)y(x) + f(x) the domain of interest [a,b] is divided into an appropriate number L of subintervals. The coefficient matrix A(x) is replaced by its value Ak at a point xk within the Kth subinterval, thus replacing the original system by the L discretized systems yk(x) = Akyk(x) + fk(x), k = 1,2,…, L. The fundamental matrix solution Φk(x, xk) over each subinterval is found by computing the eigenvalues and eigenvectors of each Ak. By matching the solutions yk(x) at the L - 1 equispaced grid points defining the limits of the subintervals and the boundary conditions, the two-point problem is reduced to solving a system of linear algebraic equations for the matching constants characterizing the different yk(x). The values of y1(a) and yL(b) are used to calculate the missing boundary conditions. For initial-value problems this method is equivalent to a one-step method for generating approximate solutions. By means of a coordinate transformation, as in the multiple shooting method,1 the method becomes particularly suitable for stiff systems of linear ordinary differential equations. Five examples are discussed to illustrate the viability of the method.
Additional Material:
8 Tab.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/nme.1620280514
