Numerical Solution of the 1D Advection-Diffusion Equation Using Standard and Nonstandard Finite Difference Schemes

@article{Appadu2013NumericalSO,
  title={Numerical Solution of the 1D Advection-Diffusion Equation Using Standard and Nonstandard Finite Difference Schemes},
  author={A. R. Appadu},
  journal={J. Applied Mathematics},
  year={2013},
  volume={2013},
  pages={734374:1-734374:14}
}
Abstract In this work, three numerical methods have been used to solve the one-dimensional advection-diffusion equation with constant coefficients. This partial differential equation is dissipative but not dispersive. We consider the Lax-Wendroff scheme which is explicit, the Crank-Nicolson scheme which is implicit as well as a Non-Standard Finite Difference scheme [14]. We solve a 1-D numerical experiment with specified initial and boundary conditions, for which the exact solution is known… CONTINUE READING

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