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Showing content from https://TheAlgorithms.github.io/C-Plus-Plus/db/dd3/ode__forward__euler_8cpp_source.html below:

TheAlgorithms/C++: numerical_methods/ode_forward_euler.cpp Source File

Go to the documentation of this file. 54void problem

(

const double

&x, std::valarray<double> *y,

55

std::valarray<double> *dy) {

56 const double

omega = 1.F;

58

(*dy)[1] = -omega * omega * (*y)[0];

68

y[0][0] = std::cos(x);

69

y[0][1] = -std::sin(x);

87

std::valarray<double> *y, std::valarray<double> *dy) {

103

std::valarray<double> *y,

bool

save_to_file =

false

) {

104

std::valarray<double> dy = *y;

108

fp.open(

"forward_euler.csv"

, std::ofstream::out);

110

std::perror(

"Error! "

);

114

std::size_t L = y->size();

117

std::clock_t t1 = std::clock();

121 if

(save_to_file && fp.is_open()) {

124 for

(

int

i = 0; i < L - 1; i++) {

125

fp << y[0][i] <<

","

;

127

fp << y[0][L - 1] <<

"\n"

;

132

}

while

(x <= x_max);

134

std::clock_t t2 = std::clock();

140 return static_cast<double>

(t2 - t1) / CLOCKS_PER_SEC;

154 const double

&step_size,

155 const

std::valarray<double> &Y0) {

157

std::valarray<double> y(Y0);

159

std::ofstream fp(

"exact.csv"

, std::ostream::out);

161

std::perror(

"Error! "

);

164

std::cout <<

"Finding exact solution\n"

;

166

std::clock_t t1 = std::clock();

169 for

(

int

i = 0; i < y.size() - 1; i++) {

172

fp << y[y.size() - 1] <<

"\n"

;

177

}

while

(x <= X_MAX);

179

std::clock_t t2 = std::clock();

180 double

total_time =

static_cast<double>

(t2 - t1) / CLOCKS_PER_SEC;

181

std::cout <<

"\tTime = "

<< total_time <<

" ms\n"

;

189int main

(

int

argc,

char

*argv[]) {

192

std::valarray<double> Y0{1.f, 0.f};

193 double

step_size = NAN;

196

std::cout <<

"\nEnter the step size: "

;

197

std::cin >> step_size;

200

step_size = std::atof(argv[1]);

204 double

total_time =

forward_euler

(step_size, X0, X_MAX, &Y0,

true

);

205

std::cout <<

"\tTime = "

<< total_time <<

" ms\n"

;

int main()

Main function.

void forward_euler_step(const double dx, const double x, std::valarray< double > *y, std::valarray< double > *dy)

Compute next step approximation using the forward-Euler method.

double forward_euler(double dx, double x0, double x_max, std::valarray< double > *y, bool save_to_file=false)

Compute approximation using the forward-Euler method in the given limits.

void save_exact_solution(const double &X0, const double &X_MAX, const double &step_size, const std::valarray< double > &Y0)

void problem(const double &x, std::valarray< double > *y, std::valarray< double > *dy)

Problem statement for a system with first-order differential equations. Updates the system differenti...

void exact_solution(const double &x, std::valarray< double > *y)

Exact solution of the problem. Used for solution comparison.

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