The two dimensional heat equation - Trinity University

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The 2D heat equation Homogeneous Dirichlet boundary conditions Steady state solutionsRemarks: As we have noted previously:We have not proven this solution is unique. This requires themaximum principle.If we know the sine series expansion for f 2 (x) then we can usethe relationshipB n =1sinh nπbato avoid integral computations.(nth sine coefficient of f 2 (x))DailedaThe 2D heat equation
The 2D heat equation Homogeneous Dirichlet boundary conditions Steady state solutionsExampleExampleSolve the Dirichlet problem on the square [0,1]×[0,1], subject tothe boundary conditionsu(x,0) = 0, u(x,b) = f 2 (x), 0 < x < a,u(0,y) = u(a,y) = 0, 0 < y < b.wheref 2 (x) ={75x if 0 ≤ x ≤ 2 3 ,150(1−x) if 2 3 < x ≤ 1.DailedaThe 2D heat equation
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The two dimensional heat equation - Trinity University

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