A high-order implicit–explicit compact finite difference method for a nonlinear time-fractional Benjamin–Bona–Mahony–Burgers equation

Key Points

• Solutions show enhanced accuracy for the nonlinear equations with a focus on time-fractional dynamics.
• Key metrics indicate computational efficiency, achieving higher order accuracy across tested conditions.
• Observational analysis utilizing a high-order implicit–explicit compact finite difference method shows significant improvement.
• Improved methods may enable better modeling of complex physical phenomena associated with these equations.