Applications of numerical methods

Applications of numerical methods

1. WELCOME TO MY PRESENTATION Daffodil Internatioal University

2. SUBMITTED TO : Name : Omar Sharif Designation : Lecturer Department Department of Natural Sciences Faculty Faculty of Science and Information Technology E-mail [email protected] SUBBMITTED BY : NAME : Arafat Rahman ID: 152-15-5983 Dept of CSE SEC –B Daffodil International University

3. TOPICS : Application of Numerical Methods AND MY ACHIVEMENT

4. What is Numerical Method ? A numerical method is a complete and definite set of procedures for the solution of a problem, together with computable error estimates. The study and implementation of such methods is the province of numerical analysis. "numerical methods."

5. Types of Numerical Methods 1 .Bisection method 2. Newton Rapshon method (Newton’s Iteration method) 3. Iteration method 4. Newton’s forward interpolation formula 5. Newton’s backward interpolation formula 6. Gauss Seidel Method 7. CURVE FITTING

6. Applications Usually used in computer science for root algorithm. It is used to determine profit and loss in the company. Used for Multidimensional root finding. Solving practical technical problems using scientific and mathematical tools Network Simulation Train and Traffic signal Weather prediction Build up a algorithm

7. Numerical Method in PHOTOGRAPHY :

8. Maths and crime: Deblurring a number plate A short crime story Rana robs a bank Escapes in a getaway car Pursued by police

9. SOLUTION Find a model of the blurring process Blurring function g Original image f Blurring formula Inverting the formula we can get rid the blur BUT need to know the blurring function g

10. Inversion formula h(x) f(x) An example of Image Processing

11. Scientific computing Design and analysis of algorithms for numerically solving mathematical problems in science and engineering Considers the effect of approximations and performs error analysis modern simulations of engineering applications

12. Computational problems: attack strategy Develop mathematical model (usually requires a combination of math skills and some a priori knowledge of the system) Come up with numerical algorithm (numerical analysis skills) Implement the algorithm (software skills) Run, debug, test the software Visualize the results Interpret and validate the results Mathematical modeling

13. Computational problems: well- posedness The problem is well-posed , if (a) solution exists (b) it is unique (c) it depends continuously on problem data Simplification strategies: Infinite finite Nonlinear linear High-order low-order Only approximate solution can be obtained this way!

14. What computers can’t do Solve (by reasoning) general mathematical problems  t hey can only repetitively apply arithmetic primitives to input. Solve problems exactly . Represent all numbers. Only a finite subset of the numbers between 0 and 1 can be represented.

15. MY ACHIVEMENT

16. THANK YOU