The method of normal splines for linear implicit differential equations of second order.
The Numerical Computation of Compressed States of Nonlinearly Elastic Anisotropic Plates.
The numerical method for solving differential equations of Lane-Emden type by Padé approximation.
The numerical method of solving ordinary differential equations with the Cauchy initial condition
The Numerical Solution of Boundary Value Problems for Second Order Functional Differential Equations by Finite Differences.
The numerical solution of boundary-value problems for differential equations with state dependent deviating arguments
A numerical method for the solution of a second order boundary value problem for differential equation with state dependent deviating argument is studied. Second-order convergence is established and a theorem about the asymptotic expansion of global discretization error is given. This theorem makes it possible to improve the accuracy of the numerical solution by using Richardson extrapolation which results in a convergent method of order three. This is in contrast to boundary value problems for...
The Numerical Solution Of Elliptic Partial Differential Equations By The Method Of Lines.
The numerical solution of linear time-varying DAEs with index 2 by IRK methods.
The Numerical Solution of Stiff IVPs in ODEs Using Modified Second Derivative BDF
This paper considers modified second derivative BDF (MSD-BDF) for the numerical solution of stiff initial value problems (IVPs) in ordinary differential equations (ODEs). The methods are A-stable for step length .
The numerical treatment of perturbed bifurcation in boundary value problems
The numerical treatment of stiff initial value problems
The -product approach for linear ODEs: A numerical study of the scalar case
Solving systems of non-autonomous ordinary differential equations (ODE) is a crucial and often challenging problem. Recently a new approach was introduced based on a generalization of the Volterra composition. In this work, we explain the main ideas at the core of this approach in the simpler setting of a scalar ODE. Understanding the scalar case is fundamental since the method can be straightforwardly extended to the more challenging problem of systems of ODEs. Numerical examples illustrate the...
The RCWA method - A case study with open questions and perspectives of algebraic computations.
The shooting method and multiple solutions of two/multi-point BVPs of second-order ODE.
The shooting method and nonhomogeneous multipoint bvps of second-order ODE.
The solution existence and convergence analysis for linear and nonlinear differential-operator equations in Banach spaces within the Calogero type projection-algebraic scheme of discrete approximations
The projection-algebraic approach of the Calogero type for discrete approximations of linear and nonlinear differential operator equations in Banach spaces is studied. The solution convergence and realizability properties of the related approximating schemes are analyzed. For the limiting-dense approximating scheme of linear differential operator equations a new convergence theorem is stated. In the case of nonlinear differential operator equations the effective convergence conditions for the approximated...
The spectral approximation for the shock layer problems.
The stability analysis of a discretized pantograph equation
The paper deals with a difference equation arising from the scalar pantograph equation via the backward Euler discretization. A case when the solution tends to zero but after reaching a certain index it loses this tendency is discussed. We analyse this problem and estimate the value of such an index. Furthermore, we show that the utilized proof technique enables us to investigate some other numerical formulae, too.
The Stability Function for Multistep Collocation Methods.
The structure of spline collocation matrix for singularly perturbation problems with two small parameters.