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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, difference equations
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R1) Lecture notes
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2
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Stability analysis, convergence analysis
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R1) Lecture notes
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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) Lecture notes
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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) Lecture notes
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5
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Extrapolation method: Euler extrapolation, stability analysis
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R1) Lecture notes
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6
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Implicit Runge-Kutta Methods, Obrechkoff methods
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R1) Lecture notes
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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) Lecture notes
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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) Lecture notes
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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) Lecture notes
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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) Lecture notes
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11
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Predictor-corrector methods, implicit multi-step methods, (P(CE)^m)E method, Adams predictor-corrector method, modified methods
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R1) Lecture notes
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12
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Hybrid methods: one-step hybrid methods, two-step hybrid methods
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R1) Lecture notes
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13
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Higher order differential equations, hybrid methods, Obrachkoff methods, adaptive methods, Nonregular step methods: Adams-Bashforth methods, Adams-Moulton methods
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R1) Lecture notes
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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) Lecture notes
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Prerequisites
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-
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Language of Instruction
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Turkish
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Responsible
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Prof. Dr. Ahmet Yaşar ÖZBAN
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Instructors
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-
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Assistants
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[1] Assist. Prof. Dr. Şerifenur CEBESOY ERDAL
[2] Teach. Assist. Dr. Harun BALDEMİR
[3] Teach. Assist. Dr. Emel BOLAT YEŞİLOVA
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Resources
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[1] Lecture notes
[2] Numerical Solution of Differential Equations, M. K. Jain, Halsted Press, 1985.
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Supplementary Book
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Numerical Solution of Differential Equations, M. K. Jain, Halsted Press, 1985.
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Goals
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To teach the methods and their analysis for finding numerical solutions of partial differential equations
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Content
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Initial value problems, difference equations, Stability analysis, convergence analysis, Runge-Kutta methods, Extrapolation method, stability analysis, stiff systems, Adaptive methods, Multi-step methods, General linear multi-step methods, Predictor-corrector methods, Hybrid methods, Numerical methods for boundary value problems.
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Program Learning Outcomes |
Level of Contribution |
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1
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Having advanced theoretical and applied knowledge in the basic areas of mathematics
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4
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2
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Ability of abstract thinking
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-
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3
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To be able to use the acquired mathematical knowledge in the process of defining, analyzing and separating the problem encountered into solution stages.
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-
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4
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Associating mathematical achievements with different disciplines and applying them in real life
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-
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5
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Ability to work independently in a problem or project that requires knowledge of mathematics
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5
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6
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Ability to work harmoniously and effectively in national or international teams and take responsibility
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3
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7
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Having the skills to critically evaluate and advance the knowledge gained from different areas of mathematics
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-
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8
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To be able to determine what kind of knowledge learning the problem faced and to direct this knowledge learning process.
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-
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9
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To adopt the necessity of learning constantly by observing the improvement of scientific accumulation over time
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-
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10
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Ability to verbally and in writing convey thoughts on mathematical issues, and solution proposals to problems, to experts or non-experts.
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-
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11
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Being able to produce projects and organize events with social responsibility awareness
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-
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12
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Being able to follow publications in the field of mathematics and exchange information with colleagues by using a foreign language at least at the European Language Portfolio B1 General Level
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-
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13
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Ability to use computer software (at least at the Advanced Level of European Computer Use License), information and communication technologies for solving mathematical problems, transferring ideas and results
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-
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14
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Being conscious of acting in accordance with social, scientific, cultural and ethical values
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-
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