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## Graduate School of Science and Engineering

Science of Environment and Mathematical Modeling

### Computational Mathematics Laboratory

Study the new world opened by computational mathematics

#### Staff

#### Research Topics

- Numerical analysis of nonlinear phenomena such as blow-up or bifurcation phenomena
- Numerical analysis of existence or smoothness of solutions of differential and integral equations
- Development of numerical methods for numerical analysis
- Development of numerical methods for highly accurate numerical solutions
- Large-scale parallel computing in multiple precision
- Direct numerical simulation of inverse problems

#### Research Contents

Numerical computation is an important tool for investigation of concrete behaviors of solutions of differential and integral equations. Numerical results often give useful information for theoretical analysis. In our laboratory numerical computation is carried out for getting theoretically interesting behaviors of solutions. Numerical methods which are necessary for such numerical computation are developed. By using multiple-precision arithmetic defiant attempts are done such as direct numerical simulation of inverse problems.

#### Keywords

- Numerical analysis
- Differential and integral equations
- Multiple-precision computation
- Spectral methods
- Large-scale parallel computing
- Inverse problems