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Taylor‘s Method

Taylor‘s Method. 수학과 2004023371 이창혁. 수학과 2008019455 김종현. 수학과 2008057903 조예원. Main Theorem. Taylor’s Theorem. Subject for Inquiry. Problem 1.

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Taylor‘s Method

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  1. Taylor‘s Method 수학과 2004023371 이창혁 수학과 2008019455 김종현 수학과 2008057903 조예원

  2. Main Theorem Taylor’s Theorem

  3. Subject for Inquiry • Problem 1 • Compute the Taylor polynomials of degree 4 for the solutions to the given initial value problems. Use these Taylor polynomials to approximate the solution at x = 1. • (i) dy/dx = x – 2y; y(0) = 1. (ii) dy/dx = y(2 – y); y(0) = 4. • Problem 2 Compare the use of Euler’s method with that of Taylor series to approximate the solution Ф(x) to the initial value problem dy/dx + y = cos x – sin x; y(0) = 0.

  4. Result of Research (1/12) • (i) dy/dx = x – 2y; y(0) = 1

  5. Result of Research (2/12) • Graphs

  6. Result of Research (3/12) • Codes

  7. Result of Research (4/12) • (ii) dy/dx = y(2 – y); y(0) = 4.

  8. Result of Research (5/12) • Graphs

  9. Result of Research (6/12) • Codes

  10. Result of Research (7/12) • dy/dx + y = cos x – sin x; y(0) = 0.

  11. Result of Research (8/12) • X = 1 • X = 3

  12. Result of Research (9/12) • Codes

  13. Result of Research (10/12) • Results

  14. Result of Research (11/12) • [ ] : error

  15. Result of Research (12/12) • [ ] : error

  16. Conclusion & Discussion • Taylor Method is approaching the exact value • closer than Euler Method. • Other approaching method… •  Improved Euler Method •  RungeKutta Method

  17. Thank You!

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