We analyze fully implicit and linearly implicit backward difference formula (BDF) methods for quasilinear parabolic equations, without making any assumptions on the growth or decay of the coefficient functions. We combine maximal parabolic regularity and energy estimates to derive optimal-order error bounds for the time-discrete approximation to the solution and its gradient in the maximum norm...

Using ideas of S. Wassermann on non-exact C∗-algebras and property T groups, we show that one of his examples of non-invertible C∗-extensions is not semiinvertible. To prove this, we show that a certain element vanishes in the asymptotic tensor product. We also show that a modification of the example gives a C∗-extension which is not even invertible up to homotopy. Introduction The Brown–Dougla...

We consider a two-dimensional model of double-diffusive convection and 1 its time discretisation using a second-order scheme (based on backward differentiation 2 formula for the time derivative) which treats the non-linear term explicitly. Uniform 3 bounds on the solutions of both the continuous and discrete models are derived (under 4 a timestep restriction for the discrete model), proving the...

This work presents a high order numerical method for the solution of generalized Black-Scholes model for European call option. The numerical method is derived using a two-step backward differentiation formula in the temporal discretization and a High-Order Difference approximation with Identity Expansion (HODIE) scheme in the spatial discretization. The present scheme gives second order accurac...

A linear parabolic differential equation on a moving surface is discretized in space by evolving surface finite elements and in time by backward difference formulas (BDF). Using results from Dahlquist’s G-stability theory and Nevanlinna & Odeh’s multiplier technique together with properties of the spatial semi-discretization, stability of the full discretization is proven for the BDF methods up...

Solving Ordinary Differential Equations (ODEs) by using Partitioning Block Intervalwise (PBI) technique is our aim in this paper. The PBI technique is based on Block Adams Method and Backward Differentiation Formula (BDF). Block Adams Method only use the simple iteration for solving while BDF requires Newtonlike iteration involving Jacobian matrix of ODEs which consumes a considerable amount of...

A new algorithm for numerical sensitivity analysis of ordinary differential equations (ODEs) is presented. The underlying ODE solver belongs to the Runge–Kutta family. The algorithm calculates sensitivities with respect to problem parameters and initial conditions, exploiting the special structure of the sensitivity equations. A key feature is the reuse of information already computed for the s...

Wheel-rail systems can be modelled as mechanical multibody systems with holonomic constraints. The dynamical behaviour is described by a diierential-algebraic system of index 3 in non{Hessenberg form ((10]). We discuss the eecient numerical solution of these model equations. A perturbation analysis suggests the integration of the model equations in the Gear{Gupta{Leimkuhler (GGL) formulation. T...

We propose and study a numerical method for time discretization of linear and semilinear integro-partial differential equations that are intermediate between diffusion and wave equations, or are subdiffusive. The method uses convolution quadrature based on the second-order backward differentiation formula. Second-order error bounds of the time discretization and regularity estimates for the sol...