Introductions of Numerical analysis of differential equations appearing in the civil engineering is given. First, learn the solution of ordinary differential equation by Finite Difference Method (FDM) and its features, then, learn the solution of partial differential equations by FDM.
In this class, as well as learning the basic theoretical aspects of the numerical analysis method, we aim to learn the practical skill of numerical analysis through the computational practice of the programing.
I. Acquire a skill to choose the appropriate numerical method depending on the problem.
II. Learn the basic knowledge on the typical numerical methods (advantages and disadvantages of each method).
III. Acquire a practical skill to implement the programing code.
FDM solution of ordinary and partially differential equations, Explicit and Implicit, Interpolation, Finite Difference Approximation of gradients, Numerical error, Programing
|Intercultural skills||Communication skills||Specialist skills||Critical thinking skills||Practical and/or problem-solving skills|
Lecture in the lecture room and practice in the computer practice room are done alternatively.
|Course schedule||Required learning|
|Class 1||FDM Solution of ODE - Methods to calculate time evolution||Learn some numerical method to calculate time evolution from ODE.|
|Class 2||FDM Solution of ODE - Programing practice||Implement a programing code to solve the ODE|
|Class 3||FDM Solution of PDE - Diffusion equation||Learn FDM to solve the diffusion equation.|
|Class 4||FDM Solution of PDE - Programing practice||Implement a programing code to solve the Diffusion equation.|
|Class 5||FDM Solution of PDE - Advection equation||Learn FDM to solve the advection equation.|
|Class 6||FDM Solution of PDE - Programing practice||Implement a programing code to solve the Advection equation.|
|Class 7||FDM Solution of PDE - Poisson equation and linear simultaneous equations||Learn FDM to solve the Poisson equation and linear simultaneous equations.|
|Class 8||FDM Solution of PDE - Programing practice||Implement a programing code to solve the Poisson equation.|
A textbook is not specified. Some materials will be distributed in each class.
Based on a report submitted in the end of class, understanding of "theory and features of FDM" and acquiring of "skill of programing" are evaluated.
Take a credit of "Computers and Fundamental Programming".