Find the root of the coupled equations x+2cosx+y-1=0 2x-siny-8=0 by the Newton-Ralphson method. (a) Put the...

 

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Find the root of the coupled equations x²+2cosx+y-1=0 2x³-siny-8=0 by the Newton-Ralphson method. (a) Put the iteration formula in the matrix form Az₁ = b₁, Ar where "i" is the iteration index, and Z= so that the improved root is (see lecture notes Ay as well as recitation notes) x = x + Ar =y,+Ay=1, 2, 3,4........ Find the expressions for the coefficient matrix A, and the column b₁, which only depend on x,,y, (10 points). (b) with the initial guess [,]=[1.0,2.0], and the requirement that the approximate relative percentage errors for both x,y to be less or equal to 0.005 (that is, <0.005; <0.005), find the approximate root by modifying the MATLAB program given in Example 3-5 (lectured in recitation of week of Jan. 30, 2023) (10 points). Find the root of the coupled equations x²+2cosx+y-1=0 2x³-siny-8=0 by the Newton-Ralphson method. (a) Put the iteration formula in the matrix form Az₁ = b₁, Ar where "i" is the iteration index, and Z= so that the improved root is (see lecture notes Ay as well as recitation notes) x = x + Ar =y,+Ay=1, 2, 3,4........ Find the expressions for the coefficient matrix A, and the column b₁, which only depend on x,,y, (10 points). (b) with the initial guess [,]=[1.0,2.0], and the requirement that the approximate relative percentage errors for both x,y to be less or equal to 0.005 (that is, <0.005; <0.005), find the approximate root by modifying the MATLAB program given in Example 3-5 (lectured in recitation of week of Jan. 30, 2023) (10 points).

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Initial guess X 10 20 Tolerance for approximate rela... View the full answer