scholarly journals An Alternating Direction Method of Multipliers for the Numerical Solution of a Fully Nonlinear Partial Differential Equation Involving the Jacobian Determinant

2018 ◽  
Vol 40 (1) ◽  
pp. A52-A80 ◽  
Author(s):  
Alexandre Caboussat ◽  
Roland Glowinski
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Numerical Solution ◽  
Nonlinear Partial Differential Equation ◽  
Alternating Direction Method ◽  
Jacobian Determinant ◽  
Method Of Multipliers ◽  
Partial Differential ◽  
Fully Nonlinear ◽  
Alternating Direction

scholarly journals An Efficient Alternating Direction Explicit Method for Solving a Nonlinear Partial Differential Equation

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Somayeh Pourghanbar ◽  
Jalil Manafian ◽  
Mojtaba Ranjbar ◽  
Aynura Aliyeva ◽  
Yusif S. Gasimov
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Finite Difference ◽  
Nonlinear Partial Differential Equation ◽  
Finite Difference Schemes ◽  
Explicit Method ◽  
Partial Differential ◽  
Unconditionally Stable ◽  
Elapsed Time ◽  
Alternating Direction

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.

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