Numerical solutions to problems differ from their analytical counterparts. Why? The reason for the difference is that most numerical computations involve error. There are two main types of error that can arise. The first, called roundoff error, arises from the fact that computers do not store real numbers instead they store a subset of real numbers: floatingpoint numbers. Thus the solution of c...

A new block method of order two for the numerical solution of initial value problems is derived. This method is similar to the block Trapezoidal rule [12] , where the low power of the block size appear in the principal local truncation error. Direct comparison with result relating to the block Trapezoidal rule results obtained in [1] is made.

Truncation-error analysis is a reliable tool in predicting convergence rates of discretization errors on regular smooth grids. However, it is often misleading in application to finitevolume discretization schemes on irregular (e.g., unstructured) grids. Convergence of truncation errors severely degrades on general irregular grids; a design-order convergence can be achieved only on grids with a ...

Thom's vorticity condition for solving the incompressible Navier-Stokes equations is generally known as a rst-order method since the local truncation error for the value of boundary vorticity is rst order accurate. In the present paper, it is shown that convergence in the boundary vorticity is actually second order for steady problems and for time-dependent problems when t > 0. The result is pr...

In some long term studies, a series of dependent and possibly truncated lifetime data may be observed. Suppose that the lifetimes have a common continuous distribution function F. A popular stochastic measure of the distance between the density function f of the lifetimes and its kernel estimate fn is the integrated square error (ISE). In this paper, we derive a central limit theorem for t...

This paper presents the comparison of implicit scheme and modied for solving parabolic partial dierential equations, is compared with using its stability, local truncation error, derivation numerical examples. Following this, it was discovered that can be used as an alternative to problems on equations.