Numerical solution of boundary value problems by least squares
Numerical solution of boundary value problems by means of B-splines
Numerical solution of boundary value problems for selfadjoint differential equations of th order
The paper is devoted to solving boundary value problems for self-adjoint linear differential equations of th order in the case that the corresponding differential operator is self-adjoint and positive semidefinite. The method proposed consists in transforming the original problem to solving several initial value problems for certain systems of first order ODEs. Even if this approach may be used for quite general linear boundary value problems, the new algorithms described here exploit the special...
Numerical solution of Cauchy type singular integral equations by use of the Lobatto-Jacobi numerical integration rule
The Lobatto-Jacobi numerical integration rule can be extended so as to apply to the numerical evaluation of Cauchy type principal value integrals and the numerical solution of singular intergral equations with Cauchy type kernels by reduction to systems of linear equations. To this end, the integrals in such a singular integral equation are replaced by sums, as if they were regular integrals, after the singular integral equation is applied at appropriately selected points of the integration interval....
Numerical solution of compressible flow
Numerical Solution of Delay Differential Equations by Uniform Corrections to an Implicit Runge-Kutta Method.
Numerical solution of differential-algebraic equations for constrained mechanical motion.
Numerical Solution of Eigentuple-Eigen vector Problems in Hilbert Spaces by a Gradient Method.
Numerical Solution of Fractional Diffusion-Wave Equation with two Space Variables by Matrix Method
Mathematics Subject Classi¯cation 2010: 26A33, 65D25, 65M06, 65Z05.In the present paper we solve space-time fractional diffusion-wave equation with two space variables, using the matrix method. Here, in particular, we give solutions to classical diffusion and wave equations and fractional diffusion and wave equations with different combinations of time and space fractional derivatives. We also plot some graphs for these problems with the help of MATLAB routines.
Numerical solution of generalized Abel integral equations by spline functions
Numerical solution of initial and singularly perturbed two-point boundary value problems using adaptive spline function approximation.
Numerical Solution of Integral Equations, Fast Algorithms and Krein-Sobolev Equation.
Numerical Solution of Integral Equations in Chebyshev Series.
Numerical solution of integral equations with finite part integrals.
Numerical solution of inverse spectral problems for Sturm-Liouville operators with discontinuous potentials
We consider Sturm-Liouville differential operators on a finite interval with discontinuous potentials having one jump. As the main result we obtain a procedure of recovering the location of the discontinuity and the height of the jump. Using our result, we apply a generalized Rundell-Sacks algorithm of Rafler and Böckmann for a more effective reconstruction of the potential and present some numerical examples.
Numerical Solution of Linear Equations with Toeplitz and Vector Toeplitz Matrices.
Numerical solution of nonlinear diffusion with finite extinction phenomenon.
Numerical Solution of Ordinary and Retarded Differential Equations with Discontinuous Derivatives.
Numerical solution of parabolic equations in high dimensions
We consider the numerical solution of diffusion problems in for and for in dimension . We use a wavelet based sparse grid space discretization with mesh-width and order , and discontinuous Galerkin time-discretization of order on a geometric sequence of many time steps. The linear systems in each time step are solved iteratively by GMRES iterations with a wavelet preconditioner. We prove that this algorithm gives an -error of for where is the total number of operations,...
Numerical solution of parabolic equations in high dimensions
We consider the numerical solution of diffusion problems in (0,T) x Ω for and for T > 0 in dimension dd ≥ 1. We use a wavelet based sparse grid space discretization with mesh-width h and order pd ≥ 1, and hp discontinuous Galerkin time-discretization of order on a geometric sequence of many time steps. The linear systems in each time step are solved iteratively by GMRES iterations with a wavelet preconditioner. We prove that this algorithm gives an L2(Ω)-error of O(N-p) for u(x,T)...