Using the numbers 3, 3, 8 and 8 once and only once, obtain the target number of 24. (use have to use 3 twice and 8 twice - 3 x 8 = 24 is not acceptable). You may use only addition, subtraction, multiplication and division (eg. no factorial). Hint: no addition in the equation.
Use Monte Carlo integration to estimate the value of the double integral, try to find....
Use Monte Carlo integration to estimate the value of the double integral (x^2+y^2)/(1+y^2) over the unit circle. Try to find a 95% confidence interval in which the true value lies? What is the exact value?
(a) Describe how the weights for the order 4 closed Newton-Cotes quadrature formula could be found. Do NOT calculate the weights. (b) What are composite quadrature rules and why are they preferred to using higher order quadrature rules? (c) What are the main characteristics of a predictor-corrector method for solving an initia ...continues
Describe how to use the Monte Carlo method to estimate the double integral of xydxdy over the area 0
Please describe how to use the Monte Carlo method to estimate the attached expression. Thanks
Euler Method solved analytically
I have a differential equation with the initial condition given by: dy/dx=y^2/x+1, where y(0)= 1. (see attached file for more detail). As requested by my question, I have used the simple and improved euler methods to estimate y(1.2) with a step size of h=0.3 to 4 decimal places. I am struggling to solve the differential e ...continues
Numerical Representation & Errors - Write Effective Algorithm
See attachments for case study and complete questions. ...there exists a double series representation {see attachment}. This double series converges slowly, and it contains many small terms whose joint effect may be big. Your task is to write an effective algorithm to calculate the values of w(p,s) for any given {see attachme ...continues
1 (a) Consider the function values... Consider a polynomial P(x) of least degree (the osculating polynomial) through the points xi=x0+i*h, i.e. polynomial that satisfies P(x0)=f0, P(x1)=f1, P'(x1)=f'(x1), P(x2)=f2 (b) Prove that df(x1)/dx = dP(x1)/dx for any smooth function f(x) (c) Construct the polynomial P(x) for the ...continues
Numerical methods - Integration rule
Derive an integration rule for the domain [0,1] based on the quadrature points x1=0, x2=1/3 and x3=1, which is exact for polynomials of degree <= 2. Please see attached for full question.
