This paper presents a modified version of the Exponential Time Differencing (ETD) method, specifically the fourth-order Runge-Kutta (ETDRK4) scheme, to address numerical instability issues in solving stiff nonlinear partial differential equations (PDEs). The modified ETD scheme generalizes the method to non-diagonal operators and is designed to improve stability and accuracy. The paper compares the performance of this modified ETD scheme with other competing methods, including implicit-explicit (IMEX) differencing, integrating factors, split-step methods, and Fornberg and Driscoll’s “sliders,” using the KdV, Kuramoto-Sivashinsky, Burgers, and Allen-Cahn equations in one space dimension. The results show that the modified ETD scheme outperforms the other methods, achieving high accuracy and efficiency for stiff PDEs, particularly in one space dimension with fixed time steps. The paper also provides MATLAB implementations for two of the equations, demonstrating the practicality and effectiveness of the modified ETD scheme.This paper presents a modified version of the Exponential Time Differencing (ETD) method, specifically the fourth-order Runge-Kutta (ETDRK4) scheme, to address numerical instability issues in solving stiff nonlinear partial differential equations (PDEs). The modified ETD scheme generalizes the method to non-diagonal operators and is designed to improve stability and accuracy. The paper compares the performance of this modified ETD scheme with other competing methods, including implicit-explicit (IMEX) differencing, integrating factors, split-step methods, and Fornberg and Driscoll’s “sliders,” using the KdV, Kuramoto-Sivashinsky, Burgers, and Allen-Cahn equations in one space dimension. The results show that the modified ETD scheme outperforms the other methods, achieving high accuracy and efficiency for stiff PDEs, particularly in one space dimension with fixed time steps. The paper also provides MATLAB implementations for two of the equations, demonstrating the practicality and effectiveness of the modified ETD scheme.