Numerical simulation of the modified regularized long wave equation by split least-squares mixed finite element method

A kind of modified regularized long wave (MRLW) equation, with some initial conditions, is solved numerically by a split least-squares mixed element method (SLSMEM), which can be split into two independent symmetric positive definite sub-schemes and solved separately. This method is useful for obtaining numerical solutions with high degree of accuracy. Numerical examples show that the SLSMEM satisfies conservation laws.