Finite difference solution of parabolic equations

Equation (6.70) is an example of a parabohc partial differential equation  

For instance, Equation (6.70) can describe the diffusion of a chemical species in porous material as a function of time and space, with diffusvity constant D. The equation can also describe the heat conduction in a material. As such it can be used to quantify how temperature is conducted throughout a material in time, with the heat diffusivity D = k/(pcp). We limit the discussion to how to solve parabolic PDEs by using the finite difference method. 

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