Buhari Alhassan

A Stiffly Stable Adaptive Fifth-Order Block Time-Stepping Method for Stiff Oscillatory Differential Equations

This paper presents an adaptive block time-stepping algorithm designed for the numerical integration of first-order stiff oscillatory problems, which typically involve multiple time scales and stringent stability conditions. The proposed method integrates a block formulation enabling the simultaneous evaluation of seve...

A Modified Third-Order Block Numerical Integration Technique for First Order Stiff and Oscillatory Differential Equations

This paper proposes a modified two-point block backward differentiation formula (MBBDF) for the numerical solution of highly stiff and oscillatory ordinary differential equations. The method achieves third-order accuracy with a reduced error constant and computes two solution values simultaneously at each step. For the...

Numerical Simulation of Stiff Systems of Ordinary Differential Equations Using a Block Extended Backward Differentiation Scheme with a Stability Control Parameter

Stiff systems of ordinary differential equations (ODEs) arise frequently in several areas of applied mathematics, science, and engineering, and their numerical integration requires methods with strong stability characteristics. In this paper, a block extended backward differentiation formula (BEBDF) with a stability co...

The Integration of Stiff Systems of Ordinary Differential Equations Using a Time-Stepping Algorithm with Off-Step Points

A Third-Order Variable Step Size Superclass of Block Backward Differentiation Formula for Efficient Solution of Highly Stiff Differential Systems

This paper develops a third-order fully implicit adaptive variable step-size superclass block backward differentiation formula (VSBBDF3) for the efficient numerical simulation of nonlinear stiff dynamical systems, including oscillatory, chaotic, and reaction-kinetics systems governed by ordinary differential equations....

The Integration of Stiff Systems of Ordinary Differential Equations Using a Time-Stepping Algorithm with Off-Step Points

Numerical experiments demonstrate that the 2SBBDFO method is an effective and reliable tool for solving stiff ODEs, and achieves higher accuracy and competitive computational efficiency compared to existing block BDF methods, particularly for smaller step sizes.