High-order methods refer to numerical techniques used in computational mathematics and scientific computing that achieve high levels of accuracy by employing high-order approximations of the solution. These methods are typically used for solving partial differential equations, where accurate solutions are important for understanding complex physical phenomena. High-order methods utilize polynomial interpolation and approximation techniques to represent the solution with a high degree of precision. This can result in faster convergence and fewer computational resources needed compared to lower-order methods. Additionally, high-order methods can provide more accurate results and capture fine details of the solution, making them particularly useful for problems with steep gradients or sharp features. Overall, high-order methods are an important research area in numerical analysis and computational science, offering a powerful tool for accurately simulating and analyzing complex systems.