Problems On Numerical Technique - Ii

Problems on Numerical Technique - II

Example-3 Approximate y and z at x = 0.1 using the Picard’s method to solve the equations

Solution: Given that y(0) = 1 and z(0) = 0.5.

In Picrad’s Method

Given x₀ = 0, y₀ = 1, and z₀ = 0.5. For First Approximation

For Second Approximation

Now when x = 0.1 y₁ = 1.05 and z = 0.5000375 and y₂ = 1.0500008 and z = 0.5000385. Hence y(0.1) = 1.0500 and z(0.1) = 0.5000. More accuracy in approximations needs more iterations.

Example-4 Use the Runge-Kutta fourth order method to find the value of y when x = 1 given that y = 1, when x = 0 (taking n = 2) and

Solution: We have

Therefore;