A WELL-CONDITIONED MATRIX FOR (kuX)X WITH DISCONTINUOUSk
M. ROONEY · International Journal for Numerical Methods in Engineering · 1996
The traditional tridiagonal matrix approximating the one-dimensional heat equation is ill-conditioned when heat conductivity changes radically. An algebraic reformulation of the tridiagonal produces a well-conditioned matrix. Additional variables are rates q=−kux at interfaces between radical changes in k. A reduced matrix amounts to a coarse approximation.