4. Individual tasks

1. Find the solution system of nonlinear equations by Newton's method.

2. Hold hand by a system of nonlinear equations by Newton's method.

3. Along with the "manual" solution provide solutions obtained by standard means of MatLab (functions fsolve).

Table 5.1 – Variants of the tasks

№	The system of two equations and two unknowns	№	tTe system of two equations and two unknowns
1	sin(x+1)-y=1.2 2x+cos(x)=2	13	x2+ y2=5 y= e-xy
2	tg(xy+0.4)= x2 0.6 x2 +2 y2=1	14	sin(x-0.6)-y=1.6 3x-cos(y)=0.9
3	cos(x-1)+y=0.5 x-cos(x)=3	15	x2+ y2=6 y= e-x
4	sin(x)+2y=2 cos(y-1)+x=0.7	16	x3+ y3=6 y= e-x
5	cos(x-1)+y=1 sin(y)+2x=1.6	17	x4+ y4=5 y= e-x
6	sin(x+1)-y=1 2x+cоs(y)=2	18	x2+ y2=1 sin(x+y)=1.2x
7	sin(x-y)-xy=0 x2- y2=0.75	19	x2+ y2=1 sin(x+y)=0.2+x
8	sin(x+y)-1.5xy=0 x2+ y2=1	20	x+cos(y-1)=0.8 y- cos(x)=2
9	sin(x-y)- xy+1=0 x2- y2=0.75	21	x2+ y2=1 x3+ y3=2
10	y=1/(x3/2+1) x2+ y2=9	22	x2+ y2=1 x - y3=0.5
11	x2+ y2=9 y=1+ e-x	23	x3+ y3=8 y=x3/2
12	x2+ y2=5 y=1-2 e-xy	24	x3+ y3=8 y=1+x3/2

5.5 Control questions

1. What is the solution of the system of nonlinear equations?

2. Solving systems of nonlinear equations with MATLAB by iterative methods.

3. What are the iterative methods for solving systems of nonlinear equations you know?

4. Give an algorithm for Newton.

5. Give an algorithm for Simple iterative.

6. Solving systems of nonlinear equations with MATLAB by function fsolve.

List of the literature

1. Турчак Л.И. Основы численных методов: Учеб. Пособие. –М.: Наука. Гл.ред.физ.-мат.Лит., 1987. -320с.

2. Джон Г.Мэтьюз, Куртис Д.Финк. Численные методы. Использование MatLab, 3-е издание. : Пер. с англ. – М.: Издательский дом «Вильямс»№, 2001. -720 с.

3. Біла Н.І., Бондаренко Л.О. Numeric Methods and Programming on Visual Basic for Applications. Конспект лекцій з дисципліни «Обчислювальна техніка та програмування» для студентів спеціальгості 8.09206.02 з англійською мовою навчання.

Appendix a.

Individual tasks to Lab number 1, 2

№	1	2
1	3x4+4x3-12x2-5=0	ln(x)+(x+1)3=0
2	2x3-9x2-60x+1=0	x2x=1
3	x4-x-1=0	x+cos(x)=1
4	2x4 - x2-10=0	x+lg(1+x)=1.5
5	3x4+8x3+6x2-10=0	lg(2+x)+2x=3
6	x4 -18x2+5x-8=0	2x+5x-3=0
7	x4+4x3-12x2+1=0	5x+3x =0
8	x4 - x3-2x2+3x-3=0	3ex=5x+2
9	3x4+4x3-12x2+1=0	5x=6x+3
10	3x4-8x3-18x2+2=0	2ex+5x-6=0
11	2x4-8x3+8x2-1=0	2arctg(x)-x+3=0
12	2x4+8x3+8x2-1=0	(x-3)  cos(x)=1
13	x4-4x3-8x2+1=0	xx= 20-9x
14	2x4-9x3-60x2+1=0	x  lg(x)=1
15	x5 +x2-5=0	tg3x=x-1
16	3x4+4x3-12x2-7=0	5x =1+e-x
17	3x4+8x3+6x2-11=0	5x =3-ex
18	x4 -18x3-10=0	arctg(x2+1/x)=x
19	3x4-8x3-18x2+2=0	tg(0.55x+0.1)=x2
20	x4 -18x -10=0	5x-6x =7
21	x4 +18x -10=0	5x-6x =3
22	x4 +18x3-6x2+x-10=0	5x =1+e-2x
23	x5 +12x3-6x2+x-10=0	7x-6x =2
24	3x5-8x3-18x2+2=0	5x =2+e-2x
25	x3 -18x -10=0	x2x=3