Adaptive finite element methods (AFEM) represent a pivotal advancement in numerical analysis by dynamically refining computational meshes to achieve greater solution accuracy. These methods are ...

In this paper the problem of delay-dependent error estimates for waveform relaxation methods applied to systems of delay-differential equations is discussed. Under ...

SIAM Journal on Numerical Analysis contains research articles on the development and analysis of numerical methods including their convergence, stability, and error ...

Backward stochastic differential equations (BSDEs) have emerged as a pivotal mathematical tool in the analysis of complex systems across finance, physics and engineering. Their formulation, generally ...

Root mean square error (rms, or its square, the variance distance) is often used to measure differences between simulated and observed fields. In this case ...

The purpose of this research is to establish methodologies of designing error-free algorithms for solving various problems in computational engineering. Focus is on the development of efficient ...

Explore numerical methods for solving constant velocity kinematics problems! In this video, we cover how to apply numerical ...

Optical systems employ a rich array of physical effects which are described by well-understood equations. However, for all but the simplest devices these equations are typically too complex to permit ...