A C...-Collocation-like Method for Two-Point Boundary Value Problems.
A Class of Simple Exponential B-Splines and Their Application to Numerical Solution to Singular Perturbation Problems.
A comparison of four- and five-point difference approximations for stabilizing the one-dimensional stationary convection-diffusion equation.
A convergence result for discrete steepest descent in weighted Sobolev spaces.
A coupled system with integral conditions.
A Finite Element Merthod Scheme for one Dimensional Elliptic Equations with High Super Convergence at the Nodes.
A Finite Element Method for a Singularly Perturbed Boundary Value Problem.
A finite element method for a two point boundary value problem with a small parameter affecting the highest derivative
A first order accuracy scheme on non-uniform mesh.
A new Green function concept for fourth-order differential equations.
A note on a linear spectral theorem for a class of first order systems in .
A Note on C° Galerkin Methods for Two-Point Boundary Problems.
A Note on Eigenvalue Problems with Eigenvalue Parameter in the Boundary Conditions.
A Petrov-Galerkin approximation of convection-diffusion and reaction-diffusion problems
A general construction of test functions in the Petrov-Galerkin method is described. Using this construction; algorithms for an approximate solution of the Dirichlet problem for the differential equation are presented and analyzed theoretically. The positive number is supposed to be much less than the discretization step and the values of . An algorithm for the corresponding two-dimensional problem is also suggested and results of numerical tests are introduced.
A posteriori error estimation for arbitrary order FEM applied to singularly perturbed one-dimensional reaction-diffusion problems
FEM discretizations of arbitrary order are considered for a singularly perturbed one-dimensional reaction-diffusion problem whose solution exhibits strong layers. A posteriori error bounds of interpolation type are derived in the maximum norm. An adaptive algorithm is devised to resolve the boundary layers. Numerical experiments complement our theoretical results.
A radially symmetric anti-maximum principle and applications to fishery management models.
A singular eigenvalue problem for second order linear ordinary differential equations.
A Sturm-Liouville problem with spectral and large parameters in boundary conditions and the associated Cauchy problem
We study a Sturm-Liouville problem containing a spectral parameter in the boundary conditions. We associate to this problem a self-adjoint operator in a Pontryagin space Π₁. Using this operator-theoretic formulation and analytic methods, we study the asymptotic behavior of the eigenvalues under the variation of a large physical parameter in the boundary conditions. The spectral analysis is applied to investigate the well-posedness and stability of the wave equation of a string.
A Two Point Boundary Value Problem with a Rapidly Oscillating Solution.
A uniformly convergent quadratic spline difference scheme for singular perturbation problems