# solve laplace's equation inside a rectangle

A thin rectangular plate has its edges ﬂxed at temper-atures zero on three sides and f (y) on the remaining side, as shown in Figure 1. Solution for 2.5.1. Exact solutions of this equation are available and the numerical results may be compared. I need help with my Laplace's equations inside a rectangle. L, 0 ? We use the general form for the solution obtained above. Laplace on rectangle Laplace on quarter circle Laplace inside circular annulus backward heat PDE is not well posed. APM 346: Problem set 2 Due Monday Oct 13,2003. This is Laplace’s equation. y ? look for the potential solving Laplace’s equation by separation of variables. Equa-tion (2.5.61) is called the solvability condition or compatibility condition for Laplace's equation. L, 0 ? Haberman 2.5.2 ; Lecture 2-5: Laplace's equation in polar coordinates (continued). Case II: Let p = -k^2. Module 27 Laplace's Equation on a Rectangle Partial Differential Equation: u t = u xx + u yy Boundary conditions: u(t,x,0) = f(x) and u(t,x,L) = g(x) u(t,0,y) = h(y) and u(t,M,y) = J(y) Initial condition: u(0,x,y) = K(x,y). X''(x) = 0 X(x) = c1x + c2 X(0) = c2 = 0 X(1) = c1 = 0 There are only trivial solutions for this case. The method for solving these problems again depends on eigenfunction expansions. Solve Laplace's equation inside a rectangle 0<=x<=L and 0<=y<=H with these boundary conditions: u(0,y)=f(y), u(L,y)=0, du/dy(x,0)=0, and du/dy(x,H)=0. x ? Equa-tion (2.5.61) is called the solvability condition or compatibility condition for Laplace's equation. (This might be say the concentration of some (dilute) chemical solute, as a function of position x, or the temperature Tin some heat conducting medium, which behaves in an entirely analogous way.) Part of my assignment is letters b., d., f., g., and h. I am so confused. = u(r; ), @u @(r;??) Hello, Homework Statement I am trying to solve Laplace's equation for the setup shown in the attachment, where f(x)=9sin(2πx)+3x and g(x)=10sin(πy)+3y. If there are two homogeneous boundary conditions in y, let Since there is no time dependence in the Laplace's equation or Poisson's equation, there is no initial conditions to be satisfied by their solutions. Given the symmetric nature of Laplace’s equation, we look for a radial solution. Y ? Question. (Laplace’s Equation on a Rectangle, Temperature and Insulation Conditions) Solve Laplace’s equation @2u @x2 + @2u @y2 on the rectangle 0

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