The two dimensional heat equation - Trinity University

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The 2D heat equation Homogeneous Dirichlet boundary conditions Steady state solutionsWe want to find steady state solutions to (7) that satisfy theDirichlet boundary conditionsu(x,0) = f 1 (x), u(x,b) = f 2 (x), 0 < x < a (8)u(0,y) = g 1 (x), u(a,y) = g 2 (y), 0 < y The problem of finding a solution to (7) - (9) is known as theDirichlet problem.We will begin by assuming f 1 = g 1 = g 2 = 0.The general solution to the Dirichlet problem will be obtainedby superposition.DailedaThe 2D heat equation
The 2D heat equation Homogeneous Dirichlet boundary conditions Steady state solutionsSolution of the Dirichlet problem on a rectangleGoal: Solve the boundary value problem∇ 2 u = 0, 0 < x < a, 0 < y < b,u(x,0) = 0, u(x,b) = f 2 (x), 0 < x < a,u(0,y) = u(a,y) = 0, 0 < y < b.Picture:DailedaThe 2D heat equation
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The two dimensional heat equation - Trinity University

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