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Abstract
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In this paper, the Saul’yev finite difference scheme for a fully nonlinear partial differential equation with initial and boundary
conditions is analyzed. -e main advantage of this scheme is that it is unconditionally stable and explicit. Consistency and
monotonicity of the scheme are discussed. Several finite difference schemes are used to compare the Saul’yev scheme with them.
Numerical illustrations are given to demonstrate the efficiency and robustness of the scheme. In each case, it is found that the
elapsed time for the Saul’yev scheme is shortest, and the solution by the Saul’yev scheme is nearest to the Crank–Nicolson method.
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