Numerical Solutions of Integral Equations on the Half Line. I. The Compact Case.
Numerical solutions of nonstandard first order initial value problems.
Numerical solutions of ordinary differential equations with quadratic trigonometric splines.
Numerical solutions of the generalized Burgers-Huxley equation by a differential quadrature method.
Numerical solutions of the mass transfer problem
Let μ and ν be two probability measures on the real line and let c be a lower semicontinuous function on the plane. The mass transfer problem consists in determining a measure ξ whose marginals coincide with μ and ν, and whose total cost ∫∫ c(x,y)dξ(x,y) is minimum. In this paper we present three algorithms to solve numerically this Monge-Kantorovitch problem when the commodity being shipped is one-dimensional and not necessarily confined to a bounded interval. We illustrate these numerical...
Numerical solutions of the nonlinear integro-differential equations.
Numerical solutions of third kind integral-algebraic equations
Numerical solutions to integral equations equivalent to differential equations with fractional time
This paper presents an approximate method of solving the fractional (in the time variable) equation which describes the processes lying between heat and wave behavior. The approximation consists in the application of a finite subspace of an infinite basis in the time variable (Galerkin method) and discretization in space variables. In the final step, a large-scale system of linear equations with a non-symmetric matrix is solved with the use of the iterative GMRES method.
Numerical solutions to the Darboux problem with functional dependence.
Numerical solvability of a class of Volterra-Hammerstein integral equations with noncompact kernels.
Numerical Stability for Solving Nonlinear Equations.
Numerical stability in dynamic elastic-plastic problems
Numerical stability in solution of ordinary differential equations
Numerical Stability of Decent Methods for Solving Linear Equations.
Numerical Stability of the Chebyshev Method for the Solution of Large Linear Systems.
Numerical stability of the cyclic Richardson iteration.
Numerical stability of the intrinsic equations for beams in time domain
Intrinsic equations represent promising approach for the description of rotor blade dynamics. They are the system of non-linear partial differential equations. Stability of numeric solution by the finite difference method is described. The stability is studied for various numerical schemes with different methods for the computation of spatial derivatives from time level (i.e., mean values of old and new time step) to (i.e., only from new time step). Stable solution was obtained only for schemes...
Numerical stability test of neutral delay differential equations.
Numerical studies of groundwater flow problems with a singularity
The paper studies mesh dependent numerical solution of groundwater problems with singularities, caused by boreholes represented as points, instead of a real radius. We show on examples, that the numerical solution of the borehole pumping problem with point source (singularity) can be related to the exact solution of a regular problem with adapted geometry of a finite borehole radius. The radius providing the fit is roughly proportional to the mesh step. Next we define a problem of fracture-rock...
Numerical studies of parameter estimation techniques for nonlinear evolution equations
We briefly discuss an abstract approximation framework and a convergence theory of parameter estimation for a general class of nonautonomous nonlinear evolution equations. A detailed discussion of the above theory has been given earlier by the authors in another paper. The application of this theory together with numerical results indicating the feasibility of this general least squares approach are presented in the context of quasilinear reaction diffusion equations.