Differential Equations Lecture Work Solutions 297

Differential Equations Lecture Work Solutions 297 - 4. Find...

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4. Find the truncation error and order for u yij 3 u ij +4 u +1 u +2 2∆ y The Taylor series are u +2 = u +2∆ yu + (2∆ y ) 2 2 u yy i j + (2∆ y ) 3 6 u yyy i j + ··· u +1 = u +∆ + (∆ y ) 2 2 u yy i j + (∆ y ) 3 6 u yyy i j + 3 u u +1 u +2 =( 1+4 3) | {z } =0 u +( 2∆ y +4∆ y ) | {z } =2∆ y u + 4∆ y 2 2 + 4∆ y 2 2 ! | {z } =0 u yy i j + 8∆ y 3 6 + 4∆ y 3 6 ! | {z } = 2 3 y 3 u yyy i j + Therefore u y ı j = 3 u u +1
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