Ad
related to: boundary value problems journal
Search results
Results From The WOW.Com Content Network
Boundary value problems are similar to initial value problems.A boundary value problem has conditions specified at the extremes ("boundaries") of the independent variable in the equation whereas an initial value problem has all of the conditions specified at the same value of the independent variable (and that value is at the lower boundary of the domain, thus the term "initial" value).
In numerical analysis, the shooting method is a method for solving a boundary value problem by reducing it to an initial value problem.It involves finding solutions to the initial value problem for different initial conditions until one finds the solution that also satisfies the boundary conditions of the boundary value problem.
In mathematics, some boundary value problems can be solved using the methods of stochastic analysis. Perhaps the most celebrated example is Shizuo Kakutani 's 1944 solution of the Dirichlet problem for the Laplace operator using Brownian motion .
The boundary value problem solver's performance suffers from this. Even stable and well-conditioned ODEs may make for unstable and ill-conditioned BVPs. A slight alteration of the initial value guess y 0 may generate an extremely large step in the ODEs solution y(t b; t a, y 0) and thus in the values of the function F whose root is sought. Non ...
The ideas behind the MFS were developed primarily by V. D. Kupradze and M. A. Alexidze in the late 1950s and early 1960s. [1] However, the method was first proposed as a computational technique much later by R. Mathon and R. L. Johnston in the late 1970s, [2] followed by a number of papers by Mathon, Johnston and Graeme Fairweather with applications.
Two numerical solutions of the nonlinear example boundary value problem ″ =, () = =. Solved by a spectral Chebyshev method and quasilinearization. The top curve used 21 interpolation nodes, and the bottom curve used 34. Both used 3 iterations.
Hilbert noted that there existed methods for solving partial differential equations where the function's values were given at the boundary, but the problem asked for methods for solving partial differential equations with more complicated conditions on the boundary (e.g., involving derivatives of the function), or for solving calculus of variation problems in more than 1 dimension (for example ...
Pages in category "Boundary value problems" The following 13 pages are in this category, out of 13 total. This list may not reflect recent changes. ...