A new linearized compact multisplitting scheme for the nonlinear convection–reaction–diffusion equations with delay

• A new transformation is introduced to convert the original equations into nonlinear delay reaction–diffusion equations.
• A linearized compact multisplitting scheme is constructed.
• The scheme is useful for modeling of convection–reaction–diffusion equations.

In this article, a new linearized compact multisplitting scheme is constructed to solve the nonlinear delay convection–reaction–diffusion equations. Firstly, the equations are converted into nonlinear delay reaction–diffusion equations by a class of novel exponential transformation. Then, the reaction–diffusion equations with delay are discreted with compact difference method in space and multisplitting scheme in time. The convergence of the scheme is proved in L∞L∞-norm. To improve the accuracy in temporal direction, a Richardson extrapolation technique is utilized. Finally, extensive numerical examples are carried out to demonstrate the accuracy of the scheme and to compare them with the numerical solutions computed by other schemes in the literature. The results show that the present scheme is accurate and efficient.