A high-resolution bi-parametric unconditionally stable ADI method for 2D uniform transmission line equation

We propose a new unconditionally stable ADI approximation of order 2 in time and 4 in space for 2D uniform transmission line equation on an unequal grid. First, we use bi-parameter mesh ratios for unequal mesh and derive a new three-level compact method (implicit) of same accuracy for the general second-order quasilinear hyperbolic partial differential equations. The stability interval for a model test problem has also been studied. For linear difference equations on an unequal mesh, ADI methods are employed. The numerical technique for the solution at first time level is derived briefly. The presented approximation is tested on various benchmark examples using unequal mesh for the confirmation and the utility of the suggested algorithm.