Introduction The design and optimization of various mechanical systems require extensive testing and experimentation. These tests and subsequent redesigns are often costly and time-consuming, presenting significant […]

Introduction Computational Fluid Dynamics (CFD) is a vital branch of fluid mechanics that employs numerical analysis and advanced algorithms to model and analyze fluid flows and […]

Project Overview The Burgers’ equation, often known as the advection equation, is widely used in computational fluid dynamics and mathematical modeling to study nonlinear wave propagation, […]

Introduction The Lax method is a numerical method used to solve partial differential equations, especially hyperbolic equations. Due to its simplicity and relative stability, it is […]

Description The wave equation is a partial differential equation that describes the behavior of waves in space and time. This equation has many applications in various […]

Description Computational Fluid Dynamics (CFD) is a branch of engineering that uses numerical methods and algorithms to model and analyze fluid flow problems. The MacCormack and […]

Introduction The heat equation, which describes heat transfer in various materials, is used in many engineering fields including mechanics, chemistry, and materials science. The Crank-Nicolson method […]

Description Laplace’s equation is a very important partial differential equation in physics and engineering, widely used in problems related to physical potentials such as electric, gravitational, […]