Numerical Methods examples

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Home > Numerical methods calculators

AtoZmath.com - Homework help (with all solution steps)
Educational Level	Secondary school, High school and College
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Problem Source	Your textbook, etc

Numerical Methods examples (Calculators)

1. Find a root an equation using
1. Bisection Method
2. False Position Method
3. Fixed Point Iteration Method
4. Newton Raphson Method
5. Secant Method
6. Muller Method
7. Halley's Method
8. Steffensen's Method
9. Ridder's Method
10. Birge-Vieta method (for `n^(th)` degree polynomial equation)
11. Bairstow method

2. Find roots of non-linear equations using
Modified Newton Raphson method (Multivariate Newton Raphson method)

3. Numerical Interpolation using
0. Best suitable formula (among 2 to 10)
1. Newton's Forward Difference formula
2. Newton's Backward Difference formula
3. Newton's Divided Difference Interpolation formula
4. Lagrange's Interpolation formula
5. Lagrange's Inverse Interpolation formula
6. Gauss Forward formula
7. Gauss Backward formula
8. Stirling's formula
9. Bessel's formula
10. Everett's formula
11. Hermite's formula
12. Missing terms in interpolation table

4.1 Numerical Differentiation using
1. Best suitable formula (among 2 to 7)
2. Newton's Forward Difference formula
3. Newton's Backward Difference formula
4. Newton's Divided Difference formula
5. Lagrange's formula
6. Stirling's formula
7. Bessel's formula

4.2 Numerical Differentiation first order and second order using
1. 2 point Forward, Backward, Central difference formula
2. 3 point Forward, Backward, Central difference formula
3. 4 point Forward, Backward, Central difference formula
4. 5 point Forward, Central difference formula

4.3 Richardson extrapolation formula for differentiation

5. Numerical Integration using
1. Trapezoidal Rule
2. Simpson's 1/3 Rule
3. Simpson's 3/8 Rule
4. Boole's Rule
5. Weddle's Rule

6.1 Solve (1st order) numerical differential equation using
1. Euler method
2. Runge-Kutta 2 method
3. Runge-Kutta 3 method
4. Runge-Kutta 4 method
5. Improved Euler method
6. Modified Euler method
7. Taylor Series method
8. Adams bashforth predictor method
9. Milne's simpson predictor corrector method

6.2 Solve (2nd order) numerical differential equation using
1. Euler method
2. Runge-Kutta 2 method
3. Runge-Kutta 3 method
4. Runge-Kutta 4 method

7. Cubic spline interpolation

Numerical Methods with example

1. Bisection, False Position, Iteration, Newton Raphson, Secant Method

Find a real root an equation using
1. Bisection Method
2. False Position Method
3. Fixed Point Iteration Method
4. Newton Raphson Method
5. Secant Method
6. Muller Method
7. Birge-Vieta method (for `n^(th)` degree polynomial equation)
8. Bairstow method

Enter an equation like...
`f(x) = 2x^3-2x-5`
`f(x) = x^3-x-1`
`f(x) = x^3+2x^2+x-1`
`f(x) = x^3-2x-5`
`f(x) = x^3-x+1`
`f(x) = cos(x)`

2. Numerical Differentiation

Numerical Differentiation using Newton's Forward, Backward Method
1. From the following table of values of x and y, obtain `(dy)/(dx)` and `(d^2y)/(dx^2)` for x = 1.2 .

x	1.0	1.2	1.4	1.6	1.8	2.0	2.2
y	2.7183	3.3201	4.0552	4.9530	6.0496	7.3891	9.0250

2. From the following table of values of x and y, obtain `(dy)/(dx)` and `(d^2y)/(dx^2)` for x = 2.2 .

x	1.0	1.2	1.4	1.6	1.8	2.0	2.2
y	2.7183	3.3201	4.0552	4.9530	6.0496	7.3891	9.0250

3. Numerical Integration

Numerical Integration using Trapezoidal, Simpson's 1/3, Simpson's 3/8 Rule

1. From the following table, find the area bounded by the curve and x axis from x=7.47 to x=7.52 using trapezodial, simplson's 1/3, simplson's 3/8 rule.

x	7.47	7.48	7.49	7.50	7.51	7.52
f(x)	1.93	1.95	1.98	2.01	2.03	2.06

2. Evaluate I = `int_0^1 (1)/(1+x) dx` by using simpson's rule with h=0.25 and h=0.5

5. Solve numerical differential equation using Euler, Runge-kutta 2, Runge-kutta 3, Runge-kutta 4 methods

1. Find y(0.1) for `y'=x-y^2`, y(0) = 1, with step length 0.1
2. Find y(0.5) for `y'=-2x-y`, y(0) = -1, with step length 0.1
3. Find y(2) for `y'=(x-y)/2`, y(0) = 1, with step length 0.2
4. Find y(0.3) for `y'=-(x*y^2+y)`, y(0) = 1, with step length 0.1
5. Find y(0.2) for `y'=-y`, y(0) = 1, with step length 0.1

4. Numerical Interpolation

Numerical Interpolation using Forward, Backward Method

1. The population of a town in decimal census was as given below. Estimate population for the year 1895.

Year	1891	1901	1911	1921	1931
Population (in Thousand)	46	66	81	93	101

2. Let y(0) = 1, y(1) = 0, y(2) = 1 and y(3) = 10. Find y(4) using newtons's forward difference formula.

3. In the table below the values of y are consecutive terms of a series of which the number 21.6 is the 6th term. Find the 1st and 10th terms of the series.

X	3	4	5	6	7	8	9
Y	2.7	6.4	12.5	21.6	34.3	51.2	72.9

4. The population of a town in decimal census was as given below. Estimate population for the year 1895.

X	0.10	0.15	0.20	0.25	0.30
tan(X)	0.1003	0.1511	0.2027	0.2553	0.3073

Find (1) tan 0.12 (2) tan 0.26

5. Certain values of x and log10x are (300,2.4771), (304,2.4829), (305,2.4843) and (307,2.4871). Find log10 301.

6. Find lagrange's Inerpolating polynomial of degree 2 approximating the function y = ln x defined by the following table of values. Hence find ln 2.7

X	2	2.5	3
ln(X)	0.69315	0.91629	1.09861

7. Using the following table find f(x) as polynomial in x

x	-1	0	3	6	7
f(x)	3	-6	39	822	1611