Quadratic spline collocation for one-dimensional linear parabolic partial differential equations

@article{Christara2009QuadraticSC,
  title={Quadratic spline collocation for one-dimensional linear parabolic partial differential equations},
  author={Christina C. Christara and Tong Chen and Duy Minh Dang},
  journal={Numerical Algorithms},
  year={2009},
  volume={53},
  pages={511-553}
}
New methods for solving general linear parabolic partial differential equations (PDEs) in one space dimension are developed. The methods combine quadratic-spline collocation for the space discretization and classical finite differences, such as Crank-Nicolson, for the time discretization. The main computational requirements of the most efficient method are the solution of one tridiagonal linear system at each time step, while the resulting errors at the gridpoints and midpoints of the space… CONTINUE READING

Citations

Publications citing this paper.
SHOWING 1-10 OF 10 CITATIONS

A Fast and Stable Algorithm for Linear Parabolic Partial Differential Equations

  • Numerical Algorithms
  • 2016
VIEW 9 EXCERPTS
CITES METHODS
HIGHLY INFLUENCED

Adaptive and High-Order Methods for Valuing American Options

VIEW 9 EXCERPTS
CITES BACKGROUND & METHODS
HIGHLY INFLUENCED

Option pricing in jump diffusion models with quadratic spline collocation

  • Applied Mathematics and Computation
  • 2016
VIEW 2 EXCERPTS
CITES BACKGROUND & METHODS

References

Publications referenced by this paper.
SHOWING 1-10 OF 16 REFERENCES

Adaptive Techniques for Spline Collocation

VIEW 3 EXCERPTS
HIGHLY INFLUENTIAL

Adaptive finite difference methods for valuing American options

D. M. DANG
  • master’s thesis, University of Toronto, Toronto, Ontario, Canada
  • 2007
VIEW 1 EXCERPT

Options

J. C. HULL
  • Futures, and Other Derivatives, Prentice Hall, sixth ed.
  • 2006
VIEW 1 EXCERPT

An efficient algorithm based on quadratic spline collocation and finite difference methods for parabolic partial differential equations

T. CHEN
  • master’s thesis, University of Toronto, Toronto, Ontario, Canada
  • 2005
VIEW 1 EXCERPT