Numerical simulation using the non-standard weighted average FDM for 2Dim variable-order Cable equation

Abstract

The fractional variable-order (VO) two-dimensional (2Dim) Cable equation is one of the most significant types of anomalous subdiffusion equations that emerge strongly in spiny neural dendrites and is solved by using an accurate numerical technique in this study. The non-standard weighted average finite difference approach is a simple proposed technique (NSWAFDM). The proposed method’s stability is investigated in depth by using the John von Neumann stability analysis approach. The arbitrary weight factor and multiple discretization schemes of the VO derivative are used to develop a specific stability criterion. To demonstrate the usefulness and accuracy of the suggested technique, numerical examples are offered.

Keywords

• 2Dim VO cable equation
• Non-standard weighted average FDM
• Stability analysis
• Numerical simulation