Partial differential equation finite differences

Smith, G.D., 1985. Numerical Solution of Partial Differential Equations Finite Difference Methods, 3rd edition. Clarendon Press. 

Smith, G.D. Numerical solution of partial differential equations. Finite difference methods. 3rd ed. Oxford Clarendon Press 1986... 

Steady state heat conduction or mass transfer in solids with constant physical properties (diffusion coefficient, thermal diffusivity, thermal conductivity, etc.) is usually represented by a linear elliptic partial differential equation. For linear parabolic partial differential equations, finite differences can be used to convert to any given partial differential equation to system of linear first order ordinary differential equations in time. In chapter 5.1, we showed how an exponential matrix method [3] [4] [5] could be used to integrate these simultaneous equations... 

Smith GD (1985) Numerical Solution of Partial Differential Equations Finite Difference Methods. Third edition. Clarendon Press, Oxford Smolarkiewicz PK (1983) A simple positive definite advection scheme with small implicit diffusion. Mon Wea Rev 11 479-486... 

Traditional methods of simulation in hydrodynamics are based on the description of a fluid field obeying to partial differential equations. Finite difference, finite elements, spectral methods are generally used to approximate the equations and they are represented in the computer by floating point numbers. The implementation of the boundary conditions is the main difficulty of these methods. 

Partial Differential Equations Finite Difference Approaches... 

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See also in sourсe #XX -- [ ]

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