A robust false transient method of lines for elliptic partial differential equations

▸ A more robust method of solving elliptic PDEs is developed and discussed. ▸ A comparison of the false transient and the proposed method is explained. ▸ Several engineering/transport examples are considered. ▸ Linear solutions are described using matrix algebra and matrix exponentials. ▸ Nonlinear problems are solved, including unstable steady state solutions.