NUMERICAL-SOLUTIONS FOR THE ONE-DIMENSIONAL HEAT-CONDUCTION EQUATION USING A SPREADSHEET

We show how to use a spreadsheet to calculate numerical solutions of t he one-dimensional time-dependent heat-conduction equation. We find th e spreadsheet to be a practical tool for numerical calculations, becau se the algorithms can be implemented simply and quickly without compli cated programming, and the spreadsheet utilities can be used not only for graphics, printing, and file management, but also for advanced mat hematical operations. We implement the explicit and the Crank-Nicholso n forms of the finite-difference approximations and discuss the geolog ical applications of both methods. We also show how to adjust these tw o algorithms to a nonhomogeneous lithosphere in which the thermal prop erties (thermal conductivity, density, and radioactive heat generation ) change from the upper crust to the lower crust and to the mantle. Th e solution is presented in a way that can fit any spreadsheet (Lotus-1 23, Quattro-Pro, Excel). In addition, a Quattro-Pro program with macro s that calculate and display the thermal evolution of the lithosphere after a thermal perturbation is enclosed in an appendix. Copyright (C) 1996 Elsevier Science Ltd