determine a cubic spline approximation that fits through data pts: P1(1; 1); P2(2; 2); P3(3; 1:5); P4(4; 3); P5(5; 2) Spline built with two functions: Y1 = a1 + a2x +a3x² + a4x³, Y2 = az + a6x+a7x² + agx³. i) Formulate 3 linear algebraic equations so y1 goes through points P1; P2 and P3 ii) Formulate 3 linear algebraic equations so y2 goes through the points P3; P4 and P5 iii) Formulate 2 linear algebraic equations so the slope and curvature are both continuous point P3.
determine a cubic spline approximation that fits through data pts: P1(1; 1); P2(2; 2); P3(3; 1:5); P4(4; 3); P5(5; 2) Spline built with two functions: Y1 = a1 + a2x +a3x² + a4x³, Y2 = az + a6x+a7x² + agx³. i) Formulate 3 linear algebraic equations so y1 goes through points P1; P2 and P3 ii) Formulate 3 linear algebraic equations so y2 goes through the points P3; P4 and P5 iii) Formulate 2 linear algebraic equations so the slope and curvature are both continuous point P3.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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plz solve question (i),(ii),(iii) with explanation and get upvotes.
Transcribed Image Text:determine a cubic spline approximation that fits through data pts:
P1(1; 1); P2(2; 2); P3(3; 1:5); P4(4; 3); P5(5; 2)
Spline built with two functions:
Y1 = a1 + azx+a3x² + a4x³,
Y2 = az + a6x +a7x² + agx³.
i) Formulate 3 linear algebraic equations so y1 goes through points P1; P2 and P3
ii) Formulate 3 linear algebraic equations so y2 goes through the points P3; P4 and P5
iii) Formulate 2 linear algebraic equations so the slope and curvature are both continuous point P3.
iv) Find the matrix A and vector b in the linear algebraic system by assembling equations from (i-iii).
v) Solve the linear system in the previous problem to determine the two cubic functions y1 and y2
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