Exponential integrators represent an innovative class of numerical methods designed to address the challenges posed by stiff differential equations. By incorporating the matrix exponential to treat ...

Fourier analysis and numerical methods have long played a pivotal role in the solution of differential equations across science and engineering. By decomposing complex functions into sums of ...

Abstract: Analytically solving complex or large-scale differential equations is often difficult or even impossible, making numerical integration methods indispensable. However, as all numerical ...

Partial differential equations (PDE) describe the behavior of fluids, structures, heat transfer, wave propagation, and other physical phenomena of scientific and engineering interest. This course ...

ABSTRACT: Fractional-order time-delay differential equations can describe many complex physical phenomena with memory or delay effects, which are widely used in the fields of cell biology, control ...

A system of ordinary differential equations (ODEs) is produced by the semi-discretize method of discretizing the advection diffusion equation (ADE). Runge-Kutta methods of the second and fourth orders ...

This study introduces a relatively new numerical technique for solving one-dimensional Fisher’s equation. The proposed numerical technique is a simple direct meshless method, which is based on the ...

The research applies fluid dynamics principles, differential equations, and numerical methods to model passenger movement during aircraft boarding and disembarkation. We focus on the Boeing 737-800 ...