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Week
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Topics
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Study Metarials
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1
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Initial value problems, esistence and uniqueness of solutions, difference equations
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R1- Section 1.1-1.3
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2
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Stability analysis, convergence analysis
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R1- Section 1.4-1.6
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3
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One-step methods: Taylor series expansion methods, convergence analysis, first and second order Runge-Kutta methods
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R1- Section 2.1-2.3
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4
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Third and fourth order Runge-Kutta methods, higher order Runge-Kutta methods, convergence and truncation error approach
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R1- Section 2.3
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5
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Extrapolation method: Euler extrapolation, stability analysis
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R1- Section 2.4-2.5
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6
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Implicit Runge-Kutta Methods, Obrechkoff methods
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R1- Section 2.6-2.7
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7
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Solutions of system of ordinary differential equations, Euler and Runge-Kutta methods, stability analysis, stiff systems
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R1- Section 2.8
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8
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Adaptive methods, Runge-Kutta-Treanor method, Liniger-Willoughby adaptation, Nystrom-Trenor adaptation
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R1- Section 2.10
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9
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Multi-step methods: Explicit multi-step methods, Adams-Bashford formulas, Nystrom formulas, Implicit multi-step methods, Adams-Moulton formulas, Milne-Simpson formulas
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R1- Section 3.1-3.3
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10
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General linear multi-step methods, truncation error approach, stability and convergence, extended error approaches
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R1- Section 3.5
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11
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Predictor-corrector methods, implicit multi-step methods, Adams predictor-corrector method, modified methods
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R1- Section 3.6
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12
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Hybrid methods: one-step hybrid methods, two-step hybrid methods
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R1- Section 3.7
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13
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Higher order differential equations, hybrid methods, Obrachkoff methods, adaptive methods, Non-uniform step methods: Adams-Bashforth methods, Adams-Moulton methods
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R1- Section 3.8-3.9
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14
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Numerical methods for boundary value problems: Shooting method, difference equations, convergence
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R1- Section 4.1-4.2, Section 4.5
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