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Abstract. We derive optimal order a posteriori error estimates for time discretizations by both the Crank–Nicolson and the Crank–Nicolson–Galerkin methods for linear and nonlinear parabolic equations. We examine both smooth and rough initial data. Our basic tool for deriving a posteriori estimates are second order Crank–Nicolson reconstructions of the piecewise linear approximate solutions. The...

Abstract In this study, a light weight portable manual food grinder for domestic use was designed and fabricated to meet grinding needs that arise from erratic power supply in Nigeria. The design analysis crank lever parameters conveyor shaft diameter were done. To make the weight, body of machine, front cover house mechanisms support stand printed with Fused deposition modelling 3D printer. le...

In this paper, the dynamic analysis of a translating five-bar linkage mechanism is presented. The model developed with applied force to crank arm resolved into two principal planes, that is, x- and y- directions resulting reaction forces moments at pin joints determined various acceleration 0, 10, 20, 30 40 m/s2 in direction as well opposite rotation. It was observed horizontal were decreasing ...

The spark timing plays a significant role in the combustion process and in deciding the engine parameters of SI engine. This paper aims at demonstrating the effect of advanced and retarded spark timing on the burn fraction variation versus crank angle, cumulative heat release rate versus the crank angle and the pressure variation as a function of crank angle with the help of MATLAB programs. Fo...

The Crank–Nicolson method can be used to solve the Black–Scholes partial differential equation in one-dimension when both accuracy and stability is of concern. In multi-dimensions, however, discretizing the computational grid with a Crank–Nicolson scheme requires significantly large storage compared to the widely adopted Operator Splitting Method (OSM). We found that symmetrizing the system of ...