In this research, discrete singular convolution, that depends on Regularized Shannon kernel, is used to look for the efficient solution of (4 + 1) dimensional nonlinear Fokas equation. The governing system of nonlinear five-dimensional Fokas equation is transformed into a system of nonlinear ordinary differential equations via discrete singular convolution quadrature technique. Consequently, the 4th order Runge–Kutta technique is employed to solve this system. The validity of this approach is achieved by comparing the obtained numerical solution with the exact solution, where the error is ≤ 1 × 10⁻⁵. Moreover, a parametric analysis is presented to examine the influence of the used approach on solitary wave solution. The computed solutions display strength, reliability and efficiency of the implemented techniques that can be effectively work for nonlinear equations in a like manner to linear models. Our treatment in this work works to solve higher dimensional nonlinear problems of physical and numerical features.