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Part of my environmental engineering education required learning the Fortran programming language to solve engineering problems that require a numerical method to solve efficiently. Here is a short list of some of the programs I've written:
Secant method and Newton's Method root finders
Gauss Elimination to solve a system of linear equations
Use of Minpack subroutine library to solve a system of nonlinear equations
Romberg integration with trapezoid rule to integrate any user-defined function
Runge-Kutta-Fehlberg (RKF) algorithm to solve a system of ordinary differential equations
RKF with shooting method to solve boundary value problem
Transient groundwater pumping problem (parabolic partial differential equation) solved with successive over-relaxation algorithm using finite difference space and time discretization.