#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;
}