Related papers: Numerical resolution of some BVP using Bernstein p…
Hamiltonian Boundary Value Methods (in short, HBVMs) is a new class of numerical methods for the efficient numerical solution of canonical Hamiltonian systems. In particular, their main feature is that of exactly preserving, for the…
We develop methods for the solution of inhomogeneous Robin type boundary value problems (BVPs) that arise for certain linear parabolic Partial Differential Equations (PDEs) on a half line, as well as a second order generalisation. We are…
We give an elementary introduction to some recent polyhedral techniques for understanding and solving systems of multivariate polynomial equations. We provide numerous concrete examples and illustrations, and assume no background in…
Well-conditioned boundary integral methods for the solution of elliptic boundary value problems (BVPs) are powerful tools for static and dynamic physical simulations. When there are many close-to-touching boundaries (eg, in complex fluids)…
To extract the approximate solutions in the case of nonlinear fractional order differential equations with the homogeneous and nonhomogeneous boundary conditions, the weighted residual method is embedded here. We exploit three methods such…
This paper is concerned with two examples on the application of the free boundary formulation to BVPs on a semi-infinite interval. In both cases we are able to provide the exact solution of both the BVP and its free boundary formulation.…
The Bernstein polynomial basis sees significant use owing to its unique properties, particularly in the field of optimal control. However, the basis is known to have a slow rate of convergence to the function it approximates. With this in…
We prove new results on the existence, non-existence, localization and multiplicity of nontrivial solutions for perturbed Hammerstein integral equations. Our approach is topological and relies on the classical fixed point index. Some of the…
A Dirichlet problem is considered for the eikonal equation in an anisotropic medium. The nonlinear boundary value problem (BVP) formulated in the present work is the limit of the diffusion-reaction problem with a reaction parameter tending…
We use a numerical-analytic technique to construct a sequence of successive approximations to the solution of a system of fractional differential equations, subject to Dirichlet boundary conditions. We prove the uniform convergence of the…
In this work, a new approach has been developed to obtain numerical solution of linear Volterra type integral equations by obtaining asymptotic approximation to solutions. Using the classical Bernoulli polynomials, a set of orthonormal…
Nonlinear two-point boundary value problems arise in numerous areas of application. The existence and number of solutions for various cases has been studied from a theoretical standpoint. These results generally rely upon growth conditions…
We present a subdivision method to solve systems of congruence equations. This method is inspired in a subdivision method, based on Bernstein forms, to solve systems of polynomial inequalities in several variables and arbitrary degrees. The…
We provide a new approach to obtain solutions of certain evolution equations set in a Banach space and equipped with nonlocal boundary conditions. From this approach we derive a family of numerical schemes for the approximation of the…
Conventionally, piecewise polynomials have been used in the boundary elements method (BEM) to approximate unknown boundary values. Since infinitely smooth radial basis functions (RBFs) are more stable and accurate than the polynomials for…
A fast and accurate algorithm for solving a Bernstein-Vandermonde linear system is presented. The algorithm is derived by using results related to the bidiagonal decomposition of the inverse of a totally positive matrix by means of Neville…
We present numerical solutions for differential equations by expanding the unknown function in terms of Chebyshev polynomials and solving a system of linear equations directly for the values of the function at the extrema (or zeros) of the…
Boundary value problems on the unit sphere arise naturally in geophysics and oceanography when scientists model a physical quantity on large scales. Robust numerical methods play an important role in solving these problems. In this article,…
We present a computer assisted method for generating existence proofs and a posteriori error bounds for solutions to two point boundary value problems (BVPs). All truncation errors are accounted for and, if combined with interval arithmetic…
Nonlinear boundary value problems (BVPs) by means of the classical Lie symmetry method are studied. A new definition of Lie invariance for BVPs is proposed by the generalization of existing those on much wider class of BVPs. A class of…