Cancer is a complex disease, responsible for a significant portion of global deaths. The
increasing prioritisation of know-why over know-how approaches in biological research has …

The nonlinear wave phenomenon constitutes a significant research field and is a capable
mathematical model for representing the transmission of energy in physical processes. This …

In this paper, we develop a compact direct radial basis function partition of unity (D-RBF-PU)
method for parabolic equations on closed surfaces. The new method involves partitioning …

This paper presents a localized meshless approach based on the radial basis function-finite
difference (RBF-FD) to find the approximation solution of the generalized Kuramoto …

The main aim of this paper is to develop a new framework of a meshless approximation for
solving numerically three nonlinear partial differential equations in biology, ie, the …

We present a fast evolution numerical algorithm for solving the Allen–Cahn (AC) equations.
One of efficient computational techniques for the AC equation is the operator splitting …

Chemotherapy is usually applied to treat advanced prostate cancer that cancer cells spread
outside the prostate gland. The treatment uses cytotoxic drugs to target cells that grow and …

In this paper, the cubic–quintic complex Ginzburg–Landau (CQCGL) equation is numerically
studied in 1D, 2D and 3D spaces. First, by the Strang splitting technique, the CQCGL …

The current paper concerns to develop a new numerical formulation to simulate the tumor
growth. The used numerical method is based on the meshless Galerkin technique in which …

This paper aims to systematically assess the local radial basis function collocation method,
structured with multiquadrics (MQs) and polyharmonic splines (PHSs), for solving steady …