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 …

It is evident that a tumor is a dangerous lump of tissue developed through the uncontrollable
division of cells, replacing healthy tissue with abnormal tissue. It is cancerous and spreads …

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 …

In this paper, we introduce second-order numerical schemes for the modified phase field
crystal (MPFC) model that are decoupled, linear, positivity-preserving, and unconditionally …

The phase field model is a popular mathematical tool for studying tumor growth. It describes
the tumor growth via marking the tumor area. Since skin tumors are usually accompanied by …

The finite element method is extremely popular in almost all fields of engineering and
scientific research due to its powerful and accessible industrial software for computational …

The hydraulic fracture is a well-known extraction technique used to extract natural gases
and oil. The techniques lead to an industrial and economic revolution and enable many …