IGNOU BCSL-058-Computer Oriented Numerical Techniques Lab, Latest Solved Assignment (July 2023 - January 2024 )
Q5. Write a C/C++ program that approximates the solution of the initial value problem: y’ = f(t, y) with y(a) =y0over[a, b] using Euler’s method. Using the program approximate the solution of the initial value problem: y’ = -2ty^2 withy(0) =1
Sol)
#include <stdio.h>
// Define the function f(t, y) = -2ty^2
double f(double t, double y) {
return -2 * t * y * y;
}
// Euler’s method for solving the initial value problem void eulerMethod(double a, double b, double h, double y0) {
double t = a;
double y = y0;
printf(“t = %lf, y = %lf\n”, t, y);
while (t < b) {
y = y + h * f(t, y);
t = t + h;
printf(“t = %lf, y = %lf\n”, t, y);
}
}
int main() {
double a = 0.0; // Initial value of t (a)
double b = 1.0; // Final value of t (b)
double h = 0.1; // Step size
double y0 = 1.0; // Initial value of y (y(a))
printf(“Approximate solution using Euler’s method:\n”);
eulerMethod(a, b, h, y0);
return 0;
}
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