Runge-Kutta methods are an important family of implicit and explicit iterative methods used for the approximation of solutions of ordinary differential equations. Explicit RungeKutta methods are unsuitable for the solution of stiff equations as their region of stability is small. Stiff equation is a differential equation for which certain numerical methods for solving the equation are numerical...

Climate modeling differs from weather forecasting primarily in terms of the spatial resolution and timescales involved. For example, weather models run at high resolution for short periods (from two to 10 days), whereas climate models run for decades or centuries of simulated time at much lower resolution to make the computations tractable. There are on the order of 100,000 to 1 million grid po...

Fast Marching represents a very efficient technique for solving front propagation problems, which can be formulated as partial differential equations with Dirichlet boundary conditions, called Eikonal equation:

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In this paper, we consider the construction of a new class of numerical methods based on the backward differentiation formulas (BDFs) that be equipped by including two off--step points. We represent these methods from general linear methods (GLMs) point of view which provides an easy process to improve their stability properties and implementation in a variable stepsize mode. These superioritie...