Course Discription |
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This course is focused on computational methods for solving ordinary and partial differential equations. Numerical solutions for ordinary differential equations, Initial value, and boundary value problems. Linear, nonlinear, and stiff ordinary differential equations. Runge-Kutta methods, multi-step methods, corrector-predictor methods, adaptive methods, shooting methods. Finite difference methods. Numerical solutions for partial differential equations. Finite difference methods for elliptic, parabolic, and hyperbolic partial differential equations. Including, Neumann’s and Dirichlet, regular and irregular boundary conditions. Explicit methods, implicit methods, Crank-Nicolson method, alternating direction implicit method (ADI), Multi-dimensional problems. |