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SOLVING SIMULTANEOUS ALGEBRA EQUATIONS

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Geosci 561: Mathematical Modeling for Geoscientists

Spring, 2003

Week

Jan. 14/16 Course overview; introduction to the Unix computer lab (Kasting)

Solving simple algebraic equations on the computer

Newtons method in 1 dimension: solving a quadratic equation

Jan. 21/23 The carbon cycle and the uptake of fossil fuel CO2 (Kasting)

Application of Newtons method to more complex systems: carbonate

equilibria

Jan. 28/30 Solving simultaneous systems of algebraic equations (Kasting)

Newtons method in N dimensions/solving matrix problems numerically

Feb. 4/6 Combined carbon cycle and greenhouse effect (Kasting)

Application: carbonate equilibria revisited

Feb. 11/13 Models of diffusion (Alley)

Ficks laws applied to heat flow

Solving Laplaces equation (steady-state heat conduction): Jacobi

iteration, Gauss-Seidel iteration, and successive over-relaxation

Feb. 18/20 Ordinary differential equations (ODEs) (Kasting)

Stiff systems of equations

Simple implicit and explicit methods for solving ODES (forward and

reverse Euler method, Crank-Nicholson method)

Feb. 25/27 Box models of the carbonate-silicate cycle (Kasting)

Application of implicit methods to a stiff, nonlinear system: the BLAG

model

Mar. 1/3 Box modeling of fossil fuel CO2 uptake (Kasting)

(No new lab--continue BLAG model)

Mar. 10-14 Spring break

Mar. 18/20 Initial conditions and boundary conditions (Alley)

internal heat generation

Mar. 25/27 Introduction to partial differential equations (PDEs) (Kasting)

Converting PDEs to systems of ODEs by finite differencing

Solving such systems using implicit methods

Lab to be determined

Apr. 1/3 Time-dependent heat conduction (Alley)

Nonsteady, 1-D heat conduction with sinusoidal surface T and constant

T at depth/tridiagonal matrix solvers

Apr. 8/10 PDE solution methods (cont.) (Kasting)

Lab to be determined

Apr. 15/17 Groundwater flow (Alley)

Numerical solution of simple groundwater flow problems

Apr. 22/24 Groundwater flow cont. (Alley)

A 29/M 1 Course wrap-up (Alley, Kasting)

Lab to be determined