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MATH450 Homework Wk4
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/** | |
Euler's Method (recursive). | |
@author Tyler Weaver | |
Compile: | |
gcc euler_r.c -o euler_r | |
Run: | |
./euler_r | |
Homework 4.8 | |
MATH 450 | |
*/ | |
#include <stdio.h> | |
#include <stdlib.h> | |
#include <stdbool.h> | |
#include <math.h> | |
#define X 0 | |
#define Y 1 | |
double func_Dy(double x, double y); // y' = (y + x)^2 | |
double func_y(double x); // y = tan(x) - x | |
double euler(double step_size, double target_x, | |
double initial_x, double initial_y, | |
double (*func)(double,double), | |
double (*actual)(double), | |
bool debug); | |
int main() | |
{ | |
const double step_size = 0.1; | |
const double initial_value[2] = {0,0}; | |
const double target_x = 2.0; | |
double output; | |
output = euler(step_size, target_x, initial_value[X], initial_value[Y], | |
func_Dy, func_y, true); | |
//printf("output = %f\r\n", output); | |
return 0; | |
} | |
double func_Dy(double x, double y) | |
{ | |
double value = pow(x+y,2); | |
return value; | |
} | |
double func_y(double x) | |
{ | |
double y = tan(x) - x; | |
return y; | |
} | |
double euler(double step_size, | |
double target_x, double x, double y, | |
double (*func)(double,double), | |
double (*actual)(double), bool debug) | |
{ | |
static bool first = true; | |
double target_y; // the output value we are looking for | |
double exact, error; | |
if(first && debug) // first time through, print the table header | |
{ | |
printf("x_n, y_n, exact, error\r\n"); | |
printf("------|--------|--------|------\r\n"); | |
first = false; | |
} | |
if(x >= target_x) // we have reached the end | |
return y; | |
else | |
{ | |
y = y + (step_size*func(x, y)); // calculate the new y value | |
x = x + step_size; // update x | |
exact = actual(x); | |
error = fabsf(exact - y); | |
if(debug) | |
printf("%3.1f, %7.3f, %7.3f, %7.3f\r\n", x,y,exact,error); // output values for debuging | |
target_y = euler(step_size,target_x,x,y,func,actual,debug); // do it again... | |
} | |
first = true; // reset the first flag | |
return target_y; // return the target_y value | |
} |
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/** | |
Improved Euler's Method (recursive). | |
@author Tyler Weaver | |
Compile: | |
gcc imp_euler.c -o imp_euler | |
Run: | |
./imp_euler | |
Homework 4.9 | |
MATH450 | |
*/ | |
#include <stdio.h> | |
#include <stdlib.h> | |
#include <stdbool.h> | |
#include <math.h> | |
#define X 0 | |
#define Y 1 | |
double func_Dy(double x, double y); // y' = (y + x)^2 | |
double func_y(double x); // y = tan(x) - x | |
double improved_euler(double step_size, double target_x, | |
double initial_x, double initial_y, | |
double (*func)(double,double), | |
double (*actual)(double), | |
bool debug); | |
int main() | |
{ | |
const double step_size = 0.1; | |
const double initial_value[2] = {0,0}; | |
const double target_x = 1.5; | |
double output; | |
output = improved_euler(step_size, target_x, initial_value[X], initial_value[Y], | |
func_Dy, func_y, true); | |
//printf("output = %f\r\n", output); | |
return 0; | |
} | |
double func_Dy(double x, double y) | |
{ | |
double value = pow(x+y,2); | |
return value; | |
} | |
double func_y(double x) | |
{ | |
double y = tan(x) - x; | |
return y; | |
} | |
double improved_euler(double step_size, | |
double target_x, double x, double y, | |
double (*func)(double,double), | |
double (*actual)(double), bool debug) | |
{ | |
static bool first = true; | |
double target_y; // the output value we are looking for | |
double exact, error; | |
double predictor; | |
if(first && debug) // first time through, print the table header | |
{ | |
printf("x_n, y_n, exact, error\r\n"); | |
printf("------|--------|--------|------\r\n"); | |
first = false; | |
} | |
if(x >= target_x) // we have reached the end | |
return y; | |
else | |
{ | |
predictor = y + (step_size*func(x, y)); // calculate the predictor | |
// now the corrector | |
y = y + 0.5*step_size*(func(x,y) + func(x+step_size,predictor)); | |
x = x + step_size; // update x | |
exact = actual(x); | |
error = fabsf(exact - y); | |
if(debug) | |
printf("%3.1f, %7.3f, %7.3f, %7.3f\r\n", x,y,exact,error); // output values for debuging | |
target_y = improved_euler(step_size,target_x,x,y,func,actual,debug); // do it again... | |
} | |
first = true; // reset the first flag | |
return target_y; // return the target_y value | |
} |
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/** | |
Runge-Kutta Method (recursive). | |
@author Tyler Weaver | |
Compile: | |
gcc runge-kutta.c -o runge-kutta | |
Run: | |
./runge-kutta | |
Homework 4.10 | |
MATH450 | |
*/ | |
#include <stdio.h> | |
#include <stdlib.h> | |
#include <stdbool.h> | |
#include <math.h> | |
#define X 0 | |
#define Y 1 | |
double func_Dy(double x, double y); // y' = (y + x)^2 | |
double func_y(double x); // y = tan(x) - x | |
double runge_kutta(double h, double target_x, | |
double initial_x, double initial_y, | |
double (*func)(double,double), | |
double (*actual)(double), | |
bool debug); | |
int main() | |
{ | |
const double h = 0.1; | |
const double initial_value[2] = {0,0}; | |
const double target_x = 1.5; | |
double output; | |
output = runge_kutta(h, target_x, initial_value[X], initial_value[Y], | |
func_Dy, func_y, true); | |
//printf("output = %f\r\n", output); | |
return 0; | |
} | |
double func_Dy(double x, double y) | |
{ | |
double value = pow(x+y,2); | |
return value; | |
} | |
double func_y(double x) | |
{ | |
double y = tan(x) - x; | |
return y; | |
} | |
double runge_kutta(double h, | |
double target_x, double x, double y, | |
double (*func)(double,double), | |
double (*actual)(double), bool debug) | |
{ | |
static bool first = true; | |
double target_y; // the output value we are looking for | |
double exact, error; | |
double k[4]; | |
if(first && debug) // first time through, print the table header | |
{ | |
printf("Runge-Kutta method\r\n"); | |
printf("x_n, y_n, exact, error\r\n"); | |
printf("------|--------|--------|------\r\n"); | |
first = false; | |
} | |
if(x >= target_x) // we have reached the end | |
return y; | |
else | |
{ | |
k[0] = h*func(x,y); // k1 | |
k[1] = h*func(x + .5*h, y + .5*k[0]); // k2 | |
k[2] = h*func(x + .5*h, y + .5*k[1]); // k3 | |
k[3] = h*func(x + h, y + k[2]); // k4 | |
x = x + h; // update x | |
y = y + (k[0] + 2*k[1] + 2*k[2] + k[3])/6.0; | |
exact = actual(x); | |
error = fabsf(exact - y); | |
if(debug) | |
printf("%3.1f, %7.3f, %7.3f, %7.3f\r\n", x,y,exact,error); // output values for debuging | |
target_y = runge_kutta(h,target_x,x,y,func,actual,debug); // do it again... | |
} | |
first = true; // reset the first flag | |
return target_y; // return the target_y value | |
} |
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