In this study, we develop the enhanced unconditionally positive finite difference method (EUPFD), and use it to solve linear and nonlinear advection–diffusion–reaction (ADR) equations. This method incorporates the proper orthogonal decomp...
In this paper, the enhanced higher-order unconditionally positive finite difference method is developed to solve the linear, non-linear and system advection diffusion reaction equations. Investigation into the effectiveness and efficiency of the prop...
This study introduces the higher-order unconditionally positive finite difference (HUPFD) methods to solve the linear, nonlinear, and system of advection–diffusion–reaction (ADR) equations. The stability and consistency of the developed m...
This study employs a novel physics-informed neural network (PINN) approach, the standard explicit finite difference method (EFDM) and unconditionally positivity preserving FDM to tackle the one-dimensional Sine–Gordon equation (SGE). Two test p...
By the iteration of the theta-formula and treating the neighbors explicitly such as the unconditionally positive finite difference (UPFD) methods, we construct a new 2-stage explicit algorithm to solve partial differential equations containing a diff...