The superposition formulas of multi-solutions to the (3+ 1)-dimensional generalized shallow
water wave-like Equation (GSWWLE) are proposed. There are arbitrary test functions in the …

In this article, we present a five-step block method coupled with an existing fourth-order
symmetric compact finite difference scheme for solving time-dependent initial-boundary …

By employing the cubic B-spline functions, a collocation approach was devised in this study
to address the Modified Regularized Long Wave (MRLW) equation. Then, we derived the …

In this paper, we investigate a two‐grid weak Galerkin method for semilinear elliptic
differential equations. The method mainly contains two steps. First, we solve the semilinear …

The hydraulic fracture is a well-known extraction technique used to extract natural gases
and oil. The techniques lead to an industrial and economic revolution and enable many …