7-3-BC-Homework.pdf - 7.3 Euleru2019s Method Homework...

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7.3 Euler’s Method Homework Problems 1 - 4, Use Euler’s Method to approximate the given value of ࢊ࢟ / ࢊ࢞ , with the given step size ο࢞ . 1. Find ࠵౦࠵? 0.5 ࠵౑࠵?࠵౦࠵? ࠵౑࠵?࠵౥࠵? = 2࠵౦࠵? ; ࠵౦࠵? 0 = 3 ; ο࠵౥࠵? = 0.1 2. Find ࠵౦࠵? 3.25 ࠵౑࠵?࠵౦࠵? ࠵౑࠵?࠵౥࠵? = ࠵౥࠵? 2 − ࠵౦࠵? ; ࠵౦࠵? 3 = 1; ο࠵౥࠵? = 0.05 3. Find ࠵౦࠵? (2) ࠵౑࠵?࠵౦࠵? ࠵౑࠵?࠵౥࠵? = ࠵౥࠵? sin ࠵౦࠵? ; ࠵౦࠵? 1 = 3 ; ο࠵౥࠵? = 0.2 4. Find ࠵౦࠵? (1) ࠵౑࠵?࠵౦࠵? ࠵౑࠵?࠵౥࠵? = cos ࠵౥࠵? + sin ࠵౦࠵? ; ࠵౦࠵? 0 = 4 ; ο࠵౥࠵? = 0.25 x ο࠵౦࠵? = ࠵౦࠵?Ԣ ( ݌ݎ࠵౒࠵?ݒ݅݋ݑݏ ) New y 0 ------------------------- 3 x ο࠵౦࠵? = ࠵౦࠵?Ԣ ( ݌ݎ࠵౒࠵?ݒ݅݋ݑݏ ) New y 3 ------------------------- 1 x ο࠵౦࠵? = ࠵౦࠵?Ԣ ( ݌ݎ࠵౒࠵?ݒ݅݋ݑݏ ) New y 1 ------------------------- 3 x ο࠵౦࠵? = ࠵౦࠵?Ԣ ( ݌ݎ࠵౒࠵?ݒ݅݋ݑݏ ) New y 0 ------------------------- 3 6
5. ࠵౑࠵?࠵౦࠵? ࠵౑࠵?࠵౥࠵? = 3 ࠵౦࠵? ; ࠵౦࠵? 0 = 2; 0 ൑ ࠵౥࠵? ൑ 4 ; ο࠵౥࠵? = 0.5 6. ࠵౑࠵?࠵౦࠵? ࠵౑࠵?࠵ౡ࠵? = ࠵౒࠵? −࠵౦࠵? ; ࠵౦࠵? 0 = 1 ; 0 ൑ ࠵ౡ࠵? ൑ 1, ο࠵ౡ࠵? = 0.1 7. Show that Euler’s method for ࠵౑࠵?࠵౦࠵? ࠵౑࠵?࠵౥࠵? = ࠵౦࠵? + cos ࠵౥࠵? with initial condition 0, 0 and using three steps with ο࠵౥࠵? = 0.1 gives ࠵౦࠵? (0.3) 0.3285 8. Approximate four points on the solution curve to ࠵౑࠵?࠵౦࠵? ࠵౑࠵?࠵౥࠵? = 2࠵౥࠵? ࠵౦࠵? starting at (0, 2) and using ο࠵౥࠵? = 0.25 Problems 5-6, Use Euler’s Method with the given step size ο࠵౥࠵? to approximate the solution of the initial-value problem over the stated interval. Sketch the graph of your approximation.

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