Boundary Value Problems and Finite Differences - Economics Assignment Help

Assignment Task

Take 1
No matter how much we would like the world to only be in one-dimension (to make our analytical math easier), the world is three-dimensional. Even more, not all engineering processes are steady state but rather change with time. Worse again, not all boundary value problems (BVPs) using finite differences (FDs)are linear, many result in a system of non-linear equations.

Even worse still, not all geometries are rectangular prisms, cylinders, or spheres, making the standard coordinate systems with standard meshing schemes difficult to implement. No matter the additional challenge, we must be able to tackle the general BVP no matter how complicated the resulting implementation may be. Thus, we must move beyond our 1D world and be able to examine boundary value problems in 2D and even 3

Multidimensional boundary value problems 

Consider a steady-state 2D BVP on the rectangular domain shown below and following the same PDE we defined last week However, this system will have no convection but does include diffusion and source terms, giving the following in 2

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