known_solution_test

#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Sat Jan 13 21:18:14 2018

@author: mac
"""

# -*- coding: utf-8 -*-
"""
Spyder Editor

This is a temporary script file.
"""
import matplotlib.pyplot as plt
import math

def gerarGrafico(X, Y, XE, YE):
    plt.plot(X,Y,':',label='Primeira linha')
    plt.plot(XE,YE,label='Solução exata')
    plt.xlabel('Eixo X')
    plt.ylabel('Eixo Y')
    plt.title('Titulo do gráfico')
    plt.legend()
    plt.show()


def metodoDePassoUnico(X, Y, n, h):
    #y_k1 = y_k + h * f(x_k, y_k)
    for k in range(0, n):
        t_k1 = X[k] + h
        y_k1 = Y[k] + h * eulerExplicito(X[k], Y[k])
        Y.append(y_k1)
        X.append(t_k1)
        
        
def eulerExplicito(x_k, y_k):
#    return y_k
    return (math.e ** (2 * x_k)) * y_k
        

def gerarPontosDaSolucaoExata(XE, YE, n, h):
    for k in range(0, n):
        xe_k1 = XE[k] + h
        ye_k1 = calcularSolucaoExata(xe_k1, h)
        XE.append(xe_k1)
        YE.append(ye_k1)
    
        
def calcularSolucaoExata(x, h):
    #return x * (math.e ** h)
    return math.e ** ((1/2) * ( (math.e ** (2*x)) - 1 ))


def main():
    #Dados iniciais
    t0 = 0
    tf = 1
    n = 32
    y0 = 1
    h = (tf - t0)/n
    
    #Lista dos resultados com C.I. adicionada
    X = [t0]
    Y = [y0]
    
    #metodo numerico
    metodoDePassoUnico(X, Y, n, h)
    
    #Lista com solucao exata    
    XE = [t0]
    YE = [y0]
    
    gerarPontosDaSolucaoExata(XE, YE, n, h)
    
    #saida
    gerarGrafico(X, Y, XE, YE)
    
main()