Asymptotic analysis provides a set of powerful techniques for approximating solutions to differential equations, particularly in cases where exact solutions are elusive. This approach is critical when ...

SIAM Journal on Applied Mathematics, Vol. 74, No. 1 (2014), pp. 60-82 (23 pages) Theoretical models for the thermal response of vertical geothermal boreholes often assume that the characteristic time ...

We provide a full asymptotic analysis of the Nörlund polynomials and Stirling polynomials. We give a general asymptotic expansion—to any desired degree of accuracy—when the parameter is not an integer ...

This paper presents a convergence analysis of Crank–Nicolson and Rannacher time-marching methods which are often used in finite difference discretizations of the Black–Scholes equations. Particular ...