Numerical Approximation of Cauchy Problems for Multidimensional Pdes with Unbounded Coefficients Arising in Financial Mathematics
نویسندگان
چکیده
In this article, we study the numerical approximation of the solution of the Cauchy problem for a multidimensional linear parabolic PDE of second order, with unbounded time and space-dependent coefficients. The PDE free term and the initial data are also allowed to grow. Under the assumption that the PDE does not degenerate, using the L2 theory of solvability in weighted Sobolev spaces, the PDE problem’s weak solution is approximated in space, with the use of finite-difference methods. Making also use of finite differences (with both the explicit and implicit schemes), the approximation in time is considered in abstract spaces for evolution equations, and then specified to the second-order parabolic PDE problem. The rate of convergence is estimated for the approximation in space and time.
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