3.6.1 Linear system of first order ode’s

Currently the solver only supports first order system of odes, that are linear and not time varying.

ode internal name "system of linear ODEs"

System of linear first order ode’s.

\[ \boldsymbol {x}^{\prime }=A\boldsymbol {x}+F\left ( \boldsymbol {x}\right ) \]

Solved using both eigenvalues and eigenvectors method and also the matrix exponential method. Only linear ode’s are supported. The following flow chart show the algorithm for two system of ode’s.

Figure 3.18: Flow chart for system of ode solver

These diagrams show the handling of repeated eigenvalues when a defective system is encountered.

Figure 3.19: repeated eigenvalue of order 2

Figure 3.20: repeated eigenvalue of order 3

Figure 3.21: repeated eigenvalue of order 4