An improved class of three stage low-dispersion low-dissipation diagonally implicit Runge-Kutta method

We propose in this work a new A-stable diagonally implicit three stage Runge-Kutta (R-K) method with highest possible reduction of dispersion error and considerably diminished dissipation inaccuracy. The scheme is conceptualized by curtailing both dissipation and dispersion error and is second order accurate. Contrary to earlier efforts of complete reduction of amplitude error we look to allow small dissipation error in this work and thereby enhance our leeway to substantially reduce dispersion error. Diverse numerical test cases exhibit benefits of the optimization process adopted here. The scheme suitable for stiff systems perform best among all three stage diagonally implicit methods discussed in this work and is quite proficient with bigger temporal step.(c) 2023 Elsevier Masson SAS. All rights reserved.