Numerical solutions of reaction-diffusion equations: Application to neural and cardiac models
2016
We describe the implementation of the explicit Euler, Crank-Nicolson, and implicit alternating direction methods for solving partial differential equations and apply these methods to obtain numerical solutions of three excitable-media models used to study neurons and cardiomyocyte dynamics. We discuss the implementation, accuracy, speed, and stability of these numerical methods.
Keywords:
- Classical mechanics
- Mathematical optimization
- Numerical analysis
- Exponential integrator
- Explicit and implicit methods
- Physics
- Numerical methods for ordinary differential equations
- Backward differentiation formula
- Multigrid method
- Numerical stability
- Numerical partial differential equations
- Theoretical physics
- Applied mathematics
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