Purchase Solution

Elliptic boundary value problem

Not what you're looking for?

Ask Custom Question

Uxx means second derivative with respect to x
Uyy means second derivative with respect to y

Uxx + Uyy = 0, 0 < x < pi, 0 < y < pi

U(x,0) = 0, U(x,pi) = 1, 0 < x < pi

U(0,y) = 0, U(pi,y) = 1 0 < y < pi

I know the problem has to be broken into 2 separate problems using U = V + W with zero conditions on 3 sides for each problem W and V. So please show the problem in this manner. Please show all work including the derivation of any eigenvalues or eigenvectors.

Purchase this Solution
Solution Summary

The solution shows to solve an elliptic boundary value problem.

Purchase this Solution
Free BrainMass Quizzes
Probability Quiz

Some questions on probability

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

View More Free Quizzes
Related BrainMass Solutions

  • Elliptic Boundary Value Problem: Lapalce and Polar Coordinates

    We have: This shows how to solve an elliptic boundary value problem with Laplace and polar coordinates. The means for the second derivative with respect to theta are given.

  • Diffusion Equations : Classify the PDE's as Elliptic, Parabolic or Hyperbolic

    (b) xuxx - uxy + yuxy +3uy = 1 Please see the attached file for the fully formatted problem. The most important thinf to recognize in determining this solution is how to look at the coefficients.

  • Calculus

    Note: Doubly periodic functions, called elliptic functions have been constructed. 2. Let f(z) be an analytic function of the complex variable z on a domain D.

  • Mathematical Modelling : Elliptic Partial Differential Equation

    20258 Mathematical Modelling : Elliptic Partial Differential Equation Please see the attached file for the fully formatted problem. Show that the PDE ...

  • Elliptic Curves

    I have also attached the problem for easier reading. ** Please see the attached file for the complete solution ** Thank you for using BrainMass.com. I hope that this helps.

  • Integrals and arc length

    To get the value of the arc length you should find corresponding value of E (, k) with these entries in the table of elliptic functions and multiply it by .

  • Concepts of Elliptic Curves

    199963 Concepts of Elliptic Curves 1. What is an elliptic curve? 2. What is the sum of three points on an elliptic curve that lie on a straight line? Hello Please find the solution in the attached file.

  • Charge plate in an ionic solution

    It is explained that the boundary condition at infinity cannot be satisfied. However, one can replace that boundary condition by another boundary condition and solve the problem that way.

  • Roots of Polynomial for a Derivative

    See attachment Problem: An elliptic curve can be written as y^2=x^3+ax+b. I need a proof for why x^3+ax+b either have 3 real roots or 1 real root and 2 complex roots.

View More Related Solutions