## A foreward finite difference procedure with exponentially increasing time steps: the method of successive squaringInland Waters/Lands Directorate, National Hydrology Research Institute, National Hydrology Research Centre, 1987 - Mathematics - 14 pages |

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2—dimensional 2nAt Applying Equation artifice At/Ax becomes boundary conditions boundary node boundary values BULLETIN calculated carries the solution CENTRE coefficients Configuration constant value converge derivative du/ds dummy variable efficient element equal Exponentially Increasing expressed Figure finite difference approximation finite difference formulation finite difference method Finite Difference Procedure forward finite difference forward method grid line HYDROLOGY RESEARCH INSTITUTE implicit Increasing Time Steps initial condition initial values internal nodes intersection invariant inverse iteration l'équation last column last row linear differential equations m(m+l matrix equation matrix form method of successive n+l n NATIONAL HYDROLOGY RESEARCH nodal values Notation number of additions number of multiplications number of nodes partial differential equations problems Procedure with Exponentially replaced represents respectively result second example shown solution forward solution of Equation standard forward STANFORD steady state solution step backwards successive squaring un+1 Vandenberg vector of constant zero