An Efficient Alternating Direction Explicit Method for Solving a Nonlinear Partial Differential Equation
Somayeh Pourghanbar, Jalil Manafian, Mojtaba Ranjbar, Aynura R. Aliyeva, Yusif S. Gasimov
Abstract
In this paper, the Saul’yev finite difference scheme for a fully nonlinear partial differential equation with initial and boundary conditions is analyzed. The 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.
Topics & Concepts
MathematicsPartial differential equationNonlinear systemMonotonic functionRobustness (evolution)Crank–Nicolson methodScheme (mathematics)Finite differenceApplied mathematicsFinite difference methodBoundary value problemConsistency (knowledge bases)Differential equationMathematical analysisGeometryPhysicsBiochemistryGeneChemistryQuantum mechanicsDifferential Equations and Numerical MethodsNumerical methods for differential equationsFractional Differential Equations Solutions