Systems of First-Order Linear Constant-Coefficient Ordinary Differential Equations

2010 ◽  
pp. 193-248
Author(s):  
Bill Goodwine
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Constant Coefficient ◽  
Order Linear ◽  
First Order

Remark on Algorithm 982: Explicit Solutions of Triangular Systems of First-order Linear Initial-value Ordinary Differential Equations with Constant Coefficients

2022 ◽  
Vol 48 (1) ◽  
pp. 1-4
Author(s):  
W. Van Snyder
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Coefficient Matrix ◽  
Explicit Solutions ◽  
Initial Value ◽  
Singular Coefficient ◽  
Order Linear ◽  
First Order ◽  
Triangular Systems ◽  
Constant Coefficients

Algorithm 982: Explicit solutions of triangular systems of first-order linear initial-value ordinary differential equations with constant coefficients provides an explicit solution for an homogeneous system, and a brief description of how to compute a solution for the inhomogeneous case. The method described is not directly useful if the coefficient matrix is singular. This remark explains more completely how to compute the solution for the inhomogeneous case and for the singular coefficient matrix case.

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