Fourth-order difference methods for the system of 2D nonlinear elliptic partial differential equations

1991 ◽  
Vol 7 (3) ◽  
pp. 227-244 ◽  
Author(s):  
M. K. Jain ◽  
R. K. Jain ◽  
R. K. Mohanty
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Fourth Order ◽  
Elliptic Partial Differential Equations ◽  
Partial Differential ◽  
Order Difference ◽  
Nonlinear Elliptic ◽  
Difference Methods

A New Fourth-Order Compact Off-Step Discretization for the System of 2D Nonlinear Elliptic Partial Differential Equations

2012 ◽  
Vol 2 (1) ◽  
pp. 59-82 ◽  
Author(s):  
R. K. Mohanty ◽  
Nikita Setia
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Fourth Order ◽  
Elliptic Partial Differential Equations ◽  
Dirichlet Boundary Conditions ◽  
Polar Coordinates ◽  
Partial Differential ◽  
Nonlinear Elliptic ◽  
Physical Problems ◽  
Grid Points

AbstractThis paper discusses a new fourth-order compact off-step discretization for the solution of a system of two-dimensional nonlinear elliptic partial differential equations subject to Dirichlet boundary conditions. New methods to obtain the fourth-order accurate numerical solution of the first order normal derivatives of the solution are also derived. In all cases, we use only nine grid points to compute the solution. The proposed methods are directly applicable to singular problems and problems in polar coordinates, which is a main attraction. The convergence analysis of the derived method is discussed in detail. Several physical problems are solved to demonstrate the usefulness of the proposed methods.

On the Dirichlet problem for weakly non-linear elliptic partial differential equations

1977 ◽  
Vol 76 (4) ◽  
pp. 283-300 ◽  
Author(s):  
E. N. Dancer
Keyword(s):  
Dirichlet Problem ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Existence Of Solutions ◽  
Elliptic Partial Differential Equations ◽  
Partial Differential ◽  
Weakly Nonlinear ◽  
Partial Derivatives ◽  
Nonlinear Elliptic ◽  
Non Linear

SynopsisWe study the existence of solutions of the Dirichlet problem for weakly nonlinear elliptic partial differential equations. We only consider cases where the nonlinearities do not depend on any partial derivatives. For these cases, we prove the existence of solutions for a wide variety of nonlinearities.

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