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In any solution to a PDE, whether analytical or numerical, you will always need as many BCs as the number of derivative steps. For examples: $$dY/dt = k Y$$ needs one BC while $$\partial Y/\partial t = k \nabla^2 Y$$ needs three BCs. The second case is germane to your problem. You will need one BC on time $t$ because one derivative is on time. You will need ...


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The proposition of this question says nothing about the size of the domain, or how the domain has been discretized. And yes, the numerical model will converge if the necessary boundary conditions between model elements have been properly described. In order to do this, all the dimensions of all elements must be properly characterized. Presumably, a ...


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