Consider the model problem below, find A and R matrices, and b and r vectors. Then...

 

 

  

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Consider the model problem below, find A and R matrices, and b and r vectors. Then find the solution: -(xu'(x))' = 4x² x EI = [0, 3] xu' (0)=0; u(L)=5; ko=0; k₁=1 u(0)=5; 9L=5; 90=1; Solve the model problem below analytically -u"=f_1=[0,3]; u(0)=u(3)=0; for ● f(x)=5 f(x)=2x f(x)=x³ A model Problem with Variable Coefficients = 1₁ap² dx aq? Aii = = [² aq? dx + Xi-1 = 1 aihi + ai+1 hi ai ai+1 " hi+1' - pxi+l Xi (-1)² h²+! (A+R)=b+r auf a -hi+l dx i=1,2,...,n-1 A₁+1 = [₁ av ₁+19 | dx = ["' + a 1 + 19 idx pxi+1 1x₁ ≈ai +1 =- (-1) hi+l di+1 hi+1 . 1 hi+l = 0, 1,...,n -hi+l A model Problem with Variable Coefficients A + R = 4 -4 -44+%22 b+r= 515 $18 (A+R)=b+r E 一般 an-an-1 + hn-1 hn-1 f(xo)h1/2 f(x₁)(hi+h₂)/2 f(x2)(h2 +h3)/2 - : f(xn-1)(hn-1 + hn)/2 f(xn)hn/2 an hn + f hn an Kogo KLBL + Ko KL Consider the model problem below, find A and R matrices, and b and r vectors. Then find the solution: -(xu'(x))' = 4x² x EI = [0, 3] xu' (0)=0; u(L)=5; ko=0; k₁=1 u(0)=5; 9L=5; 90=1; Solve the model problem below analytically -u"=f_1=[0,3]; u(0)=u(3)=0; for ● f(x)=5 f(x)=2x f(x)=x³ A model Problem with Variable Coefficients = 1₁ap² dx aq? Aii = = [² aq? dx + Xi-1 = 1 aihi + ai+1 hi ai ai+1 " hi+1' - pxi+l Xi (-1)² h²+! (A+R)=b+r auf a -hi+l dx i=1,2,...,n-1 A₁+1 = [₁ av ₁+19 | dx = ["' + a 1 + 19 idx pxi+1 1x₁ ≈ai +1 =- (-1) hi+l di+1 hi+1 . 1 hi+l = 0, 1,...,n -hi+l A model Problem with Variable Coefficients A + R = 4 -4 -44+%22 b+r= 515 $18 (A+R)=b+r E 一般 an-an-1 + hn-1 hn-1 f(xo)h1/2 f(x₁)(hi+h₂)/2 f(x2)(h2 +h3)/2 - : f(xn-1)(hn-1 + hn)/2 f(xn)hn/2 an hn + f hn an Kogo KLBL + Ko KL

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The model problem presents a boundary value problem governed by a secondorder differential equation with variable coefficients The problem we are solv... View the full answer