An exponential matrix method for solving systems of linear differential equations

2012 ◽  
Vol 36 (3) ◽  
pp. 336-348 ◽  
Author(s):  
Şuayip Yüzbaşı ◽  
Mehmet Sezer
Keyword(s):  
Differential Equations ◽  
Matrix Method ◽  
Linear Differential Equations ◽  
Linear Differential ◽  
Exponential Matrix

A Matrix Method for the Numerical Solution of Linear Differential Equations with Variable Coefficients

1957 ◽  
Vol 61 (554) ◽  
pp. 133-134
Author(s):  
E. A. Winn
Keyword(s):  
Differential Equations ◽  
Matrix Method ◽  
High Speed ◽  
Input Function ◽  
Variable Coefficients ◽  
Linear Differential Equations ◽  
Order Of Accuracy ◽  
The Matrix ◽  
Method Of Solution ◽  
Linear Differential

A method of solution of linear differential equations is derived which requires no special starting procedure, and which is, in principle at least, capable of extension to any order of accuracy. Further advantages of the method are that boundary conditions are easy to satisfy, and that the solution of families of equations differing only in the input function requires little extra computation. The method requires the reciprocation of a matrix of order equal to the number of points for which a solution is to be obtained, but this can be much simplified by suitably partitioning the matrix, and with most automatic high-speed computers the reciprocation of a matrix is in any case an easily programmed operation.

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