مشخصات پژوهش

A precise and effective numerical solution is crucial for both theoretical research and real-world applications of the viscous Burgers' equation, a basic nonlinear partial differential equation that is frequently used as a prototype model in fluid dynamics, turbulence, traffic flow, and nonlinear wave propagation. Particularly when resolving abrupt gradients or nonlinear wave interactions over extended periods of time, traditional numerical schemes—such as standard finite difference and low-order BDF methods—frequently suffer from stability issues, numerical dissipation, and poor accuracy. This calls for the creation of high-order, completely discrete algorithms that can maintain computational efficiency while attaining exceptional accuracy and stability. These issues are resolved by the suggested high-order compact backward differentiation formula (BDF) algorithm, which offers improved convergence behavior, compact spatial discretization, and increased temporal accuracy, enabling dependable simulation of the intricate dynamics present in the viscous Burgers' equation. Because it provides a strong, high-performance numerical framework that enhances both the mathematical comprehension and useful computational modeling of nonlinear viscous flow problems, this research is significant.