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Following are coupled PDEs governing the system. c1 ∂x1S11 + c2 ∂x1S22 + c3 ∂x2S12 = 0 --- (1) c2 ∂x2S11 + c1 ∂x2S22 + c3 ∂x1S12 = 0 --- (2) ∂x2 x2S11 + ∂x1 x1S22 - 2 ∂x1 x2S12 = 0 --- (3) where c1, c2, and c3 are constants. S11, S22, and S33 are 2-dimensional field. And boundary conditions are appropriately defined. In fact, Eq.(1) and (2) are the equilibrium equations and Eq.(3) is the compatibility equation of 2D static strain-stress problem. I don't have any experiences on constructing finite difference equations of coupled PDEs. How can I make finite difference equations from the system of PDEs? I need your answer.
pde differential-equations finite-difference

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