Construction of Interval Wavelet Based on Restricted Variational Principle and Its Application for Solving Differential Equations

Table 3

Influence of (10⁻³).

(10^−1)	Maximum of absolute error 𝑤𝑗𝑥−𝑥^𝑖=sin2^𝑗𝜋/𝑏−𝑎𝑥−𝑥𝑖2^𝑗𝜋/𝑏−𝑎𝑥−𝑥𝑖.(4.13)			Maximum of relative error 𝑤^′𝑗𝑥−𝑥^𝑖=⎧⎪⎪⎨⎪⎪⎩cos2^𝑗𝜋/𝑏−𝑎𝑥−𝑥𝑖𝑥−𝑥𝑖−𝑏−𝑎2^𝑗𝜋⋅sin2^𝑗𝜋/𝑏−𝑎𝑥−𝑥𝑖𝑥−𝑥^𝑖^20,,𝑥𝑥≠=𝑥𝑥𝑖𝑖,𝑤,(4.14)𝑗𝑥−𝑥^𝑖=⎧⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎩2sin2^𝑗𝜋𝑥−𝑥𝑖/𝑏−𝑎2^𝑗𝜋𝑥−𝑥𝑖^3/𝑏−𝑎−2cos2^𝑗𝜋𝑥−𝑥𝑖/𝑏−𝑎𝑥−𝑥^𝑖^2−2^𝑗𝜋sin2^𝑗𝜋𝑥−𝑥𝑖/𝑏−𝑎𝑏−𝑎𝑥−𝑥𝑖,𝑥≠𝑥^𝑖,−2^2𝑗𝜋^23𝑏−𝑎^2,𝑥=𝑥𝑖.(4.15)
	Wavelet	Quasi-wavelet	Interval wavelet	Wavelet	Quasi-wavelet	Interval wavelet
6	412.488802	207.321583	411.521362	266.324372	3.312058	6.574245
7	164.839419	151.457045	33.225063	185.349515	2.552534	5.285445
8	56.195135	63.509684	206.247916	57.747668	2.338209	3.339211
10	31.438062	33.344138	23.764024	0.798518	1.807492	1.523272