#include <stdlib.h>
#include "iostream"
#include "clocale"
#include "math.h"
#include "iomanip"
#include "fstream"
#define pi 3.1415926535
using namespace std;
int Nx, Nt;
double delta = 0.0001;
double **U;
double dx, dt;
void base() {
U=(double**)malloc(Nt*sizeof(double*));
for (int i=0; i<=Nt; i++) {
U[i]=(double*)malloc(Nx*sizeof(double));
}
}
void bounds() {
for(int n=0; n<=Nx; n++) {
U[0][n]=sin(pi*(n*dx));
}
for(int m=0; m<=Nt; m++) {
U[m][0]=exp(-m*dt)-1;
}
}
double f(double u) {
return (atan(exp(u)));
}
double f(int i, int j) {
return f(U[i][j]);
}
double df(double u) {
return exp(u)/(1+exp(2*u));
}
double equation(double u, int i, int j) {
return ((u-U[i][j+1])/dt+(f(u)-f(U[i+1][j]))/dx);
}
double dif_eq (double u) {
return 1/dt + df(u)/dx;
}
double solution(int i, int j) {
double u_prev=1, u=0;
while (abs(u-u_prev)>delta) {
u_prev = u;
u = u_prev - equation(u_prev, i ,j)/dif_eq (u_prev);
}
5
return u;
}
void maker() {
for(int i = 0; i < Nt-1; i++) {
for(int j = 0; j < Nx-1; j++) {
U[i+1][j+1]=solution(i, j);
}
}
}
int OMM1 (void) {
Nx = 100; Nt = 100;
dx = (1./Nx), dt = (1.8/Nt);
base();
bounds();
maker();
return 0;
}
return u;
}
void maker() {
for(int i = 0; i < Nt-1; i++) {
for(int j = 0; j < Nx-1; j++) {
U[i+1][j+1]=solution(i, j);
}
}
}
int OMM1 (void) {
Nx = 100; Nt = 100;
dx = (1./Nx), dt = (1.8/Nt);
base();
bounds();
maker();
return 0;
}