A SERIES SOLUTION TO A SECOND-ORDER QUASI-LINEAR PDE USING MATHEMATICA

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.