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Applied Numerical Methods

by: Kaylin Wehner

Applied Numerical Methods MATH 151A

Kaylin Wehner
GPA 3.55


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This 1 page Class Notes was uploaded by Kaylin Wehner on Friday September 4, 2015. The Class Notes belongs to MATH 151A at University of California - Los Angeles taught by Staff in Fall. Since its upload, it has received 107 views. For similar materials see /class/177819/math-151a-university-of-california-los-angeles in Mathematics (M) at University of California - Los Angeles.


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Date Created: 09/04/15
Boundary Value Problem Example lgor Yanovsky Math 151B TA Section 113 Problem 3b Write the discretization of the following boundary value problem 4 2 2 y 771 7y loga 1 1 1 1 m g 2 M1 5 W 10g27 in matrix vector notation Aw b Solution At the interior points m for i 127 N7 the differential equation to be approximated is 4 2 2 MW fay90 gym 7 10g 9 1 Since m 72 m m 712 ivymi 9 11 921 9 z 1 iiy45i7 h 12 m 7 m 712 MM W KyHmy we can write the numerical approximation to 1 as wi1 210i wiil i wi1 wiil 7 3 If 73 I hz M 2h 12101 7 logzl 2 Multiplying both sides of 2 by 712 gives 21 212 212 wiJrl 210i W71 wHi W71 7210i lOg 9 Collecting wFl w and 10111 terms7 we obtain 21 212 21 212 7lt1iigtwi71 2 72gtwi7 1 igtwi1 logm 3 The resulting system of equations can be expressed in the tridiagonal N x N matrix form Aw b7 where 212 2h 272 7177 0 0 1 9521 2h 2h 2h 47 272 717 m m2 A 0 0 7 71 2h 271 2h 2h 0 0 71 2 2 N


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