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A Series Solution To A Second-Order Quasi-Linear Pde Using Mathematica

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  • Mark Fisher

    (Federal Reserve Bank of Atlanta)

Abstract

Mathematica provides powerful tools for solving differential equations. The functions LogicalExpand and Series can be used to decompose a PDE into a system of ODEs which can then be solved numerically with DSolve, providing fast and accurate solutions. These tools are illustrated by solving the quasi-linear PDE that recursive differential utility must satisfy. When the state variables are affine, this PDE decomposes much like exponential-affine models of the term structure. By including additional terms from the series, the solution to the PDE can be approximated arbitrarily well.

Suggested Citation

  • Mark Fisher, 2000. "A Series Solution To A Second-Order Quasi-Linear Pde Using Mathematica," Computing in Economics and Finance 2000 257, Society for Computational Economics.
  • Handle: RePEc:sce:scecf0:257
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