Let us consider the di erential equation

Silent data corruptions (SDCs) are errors that corrupt the system or falsify results while remaining unnoticed by firmware or operating systems. In numerical integration solvers, SDCs that impact the accuracy of the solver are considered significant. Detecting SDCs in high-performance computing is necessary because results need to be trustworthy and the increase of the number and complexity of ...

A perception and PDE (partial di erential equation) based nonlinear transformation is proposed to process spoken words in noisy environment. The transformation was designed to reduce noise through time adaptation and spectral enhancement by evolving a focusing quadratic fourth order nonlinear PDE (the Cahn-Hillard equation). Constant, low SNR signals were adaptively decreased to reduce noise. O...

The stability in L norm is considered for the Ritz Volterra projection and some applications are presented in this paper As a result point wise error estimates are established for the nite ele ment approximation for the parabolic integro di erential equation Sobolev equations and a di usion equation with non local boundary value problem This work is supported in part by NSERC CANADA Journal of ...

We describe the structure of the nonlinear system for the coe cients of diagonally implicit multistage integration methods for ordinary di erential equations. This structure is then utilized in the search for methods of high order and stage order with a given stability function. New methods were obtained by solving the nonlinear systems by state-of-the-art software based on least squares minimi...

In this paper, by combining a new maximum principle of fourth-order equations with the theory of eigenline problems, we develop a monotone method in the presence of lower and upper solutions for some fourth-order ordinary differential equation boundary value problem. Our results indicate there is a relation between the existence of solutions of nonlinear fourth-order equation and the first eige...

This note is inspired by the paper of Bialecki, Fairweather, and Bennett [1] which studies a method for the numerical solution of u00 = f on an interval, and u = f on a rectangle, with zero boundary data; their scheme calculates that C piecewise cubic U for which U 00 (or U) agrees with f at the two (or four) Gauss quadrature points of each subdivision of the original domain. They observe that ...

We construct numerical methods to integrate ordinary di erential equations that evolve on Lie groups. These schemes are based on exponentials and iterated commutators, they are explicit and their order analysis is relatively simple. Thus we can construct group-invariant integrators of arbitrarily high order. Among other applications we show that this approach can be used to obtain new symplecti...

in this paper the solution of a second order linear dierential equations with intu-itionistic fuzzy boundary value is described. it is discussed for two dierent cases: coecientis positive crisp number and coecient is negative crisp number. here fuzzy numbers aretaken as generalized trapezoidal intutionistic fuzzy numbers (gtrifns). further a numericalexample is illustrated.