Boundary integral equation methods for solving Laplace’s equation with nonlinear boundary conditions: the smooth boundary case

Integral Equation Methods for Solving Laplace's Equation with Nonlinear Boundary Conditions: the Smooth Boundary Case

A nonlinear boundary value problem for Laplace's equation is solved numerically by using a reformulation as a nonlinear boundary integral equation. Two numerical methods are proposed and analyzed for discretizing the integral equation, both using product integration to approximate the singular integrals in the equation. The first method uses the product Simpson's rule, and the second is based o...

Integral Equation Methods for Free Boundary Problems∗

We outline a unified approach for treating free boundary problems arising in Finance using integral equation methods. Starting with the PDE formulations of the free boundary problems, we show how to derive nonlinear integral equations for the free boundaries in a variety of Finance applications. Methods to treat theoretical (existence, uniqueness) questions and analytical and numerical approxim...

Solving wave equation with spectral methods and nonreflecting boundary conditions

A multidomain spectral method for solving wave equations is presented. This method relies on the expansion of functions on basis of spherical harmonics (Y m l (θ, φ)) for the angular dependence and of Chebyshev polynomials Tn(x) for the radial part. The spherical domains consist of shells surrounding a nucleus and cover the space up to a finite radius R at which boundary conditions are imposed....

A Cantilever Equation with Nonlinear Boundary Conditions

We prove new results on the existence of positive solutions for some cantilever equation subject to nonlocal and nonlinear boundary conditions. Our main ingredient is the classical fixed point index.

The Boundary Integral Equation Method