Explain the determine yellow 9.6.3An ExampleTo illustrate the use of the technique given in the previous section, considerthe STDE1y" (x) + |1+у (") — 0,(9.297)4x2(see equation (9.263)). For this case,1f (x) = 1+4.x2(9.298)and its discretization is11+4h?k2 °fk = f("k) = f(hk):(9.299)Using the Mickens-Ramadhani finite difference discretization, we obtain1/2711+4h²k²Yk+1 + Yk-1= 2 |cosYk= 2hCoSYk,(9.300)and this gives forOkthe expression1Ok = cos (h/fk)= Cos |h.(9.301)4h2k2

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Description: Explain the determine yellow 9.6.3An ExampleTo illustrate the use of the technique given in the previous section, considerthe STDE1y" (x) + |1+у (") — 0,(9.297)4x2(see equation (9.263)). For this case,1f (x) = 1+4.x2(9.298)and its discretization is11

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9.6.3 An Example To illustrate the use of the technique given in the previous section, consider the STDE +1+ y(2) = 0, (9.297) 4x2 (see equation (9.263)). For this case, 1 f(x) = 1+ 4x2 (9.298) and its discretization is fk = f(xk) = f(hk) 1 = 1+ (9.299) %3D 4h²k2 ° Using the Mickens-Ramadhani finite difference discretization, we obtain 1/27 2 cos (hVfk) 1 1+ 4h²k2 Yk+1 + Yk-1 Yk = 2 Cos |h Yk, (9.300) and this gives for ok the expression 1/27 V fk) 1 1 + 4h?k2 Ok = COS = cos Th (9.301)

9.6.3 An Example To illustrate the use of the technique given in the previous section, consider the STDE +1+ y(2) = 0, (9.297) 4x2 (see equation (9.263)). For this case, 1 f(x) = 1+ 4x2 (9.298) and its discretization is fk = f(xk) = f(hk) 1 = 1+ (9.299) %3D 4h²k2 ° Using the Mickens-Ramadhani finite difference discretization, we obtain 1/27 2 cos (hVfk) 1 1+ 4h²k2 Yk+1 + Yk-1 Yk = 2 Cos |h Yk, (9.300) and this gives for ok the expression 1/27 V fk) 1 1 + 4h?k2 Ok = COS = cos Th (9.301)

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 64E

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