diff --git a/Figure_1.png b/Figure_1.png
new file mode 100644
index 0000000000000000000000000000000000000000..06c052dae116a480d428d3ae2dec17a8907f6e92
Binary files /dev/null and b/Figure_1.png differ
diff --git a/Figure_2.png b/Figure_2.png
new file mode 100644
index 0000000000000000000000000000000000000000..bbb8539ea7c831653736260dea37f3445bf10856
Binary files /dev/null and b/Figure_2.png differ
diff --git a/Figure_3.png b/Figure_3.png
new file mode 100644
index 0000000000000000000000000000000000000000..80159fb93bc6be7ca102d0bb0073083f07710e99
Binary files /dev/null and b/Figure_3.png differ
diff --git a/PDEsolver.cc b/PDEsolver.cc
index b347daebb554281539d678e2b17d83b8a6a25220..97d1bbe458646bcb89bae8e5f1312d76e7c48a5f 100644
--- a/PDEsolver.cc
+++ b/PDEsolver.cc
@@ -3,6 +3,7 @@
 #include <iostream>
 #include <cmath>
 using namespace std::complex_literals;
+const float PI{std::acos(-1)};
 
 void PDEerror()
 {
@@ -11,41 +12,49 @@ void PDEerror()
     float c = 1;
     float v = 0;
     int t = 0;
-    int NT = 500;
+    int NT = 2000;
 
     std::vector<std::complex<float>> infNorm;
-    for(int i=2;i<7;i++)
+    for(int i=2;i<8;i++)
     {
         int num = std::pow(2,i);
-        float T=1;
-        t = 1;
+        float T=2;
+        t = 2;
 
         // Tar fram PDE lösningen-------------------------
         // std::string inFile = "Text files/error files cos/t0_e^cos_N"+std::to_string(num)+".0.txt";
-        // std::string inFile = "Text files/files cos2pi/t0_x(10-x)_N"+std::to_string(num)+".0.txt";
         std::string inFile = "Text files/files cos2pi/t0_N"+std::to_string(num)+".0.txt";
+        // std::string inFile = "Text files/kopriva ex/phi_t0_N"+std::to_string(num)+".0.txt";
+        // std::string inFile = "Text files/files 10-x/t0_N"+std::to_string(num)+".0.txt";
+
         std::vector<std::complex<float>> pdeSolution = callPDE.FourierCollocationDriver(num,NT,T,v,c,inFile);
 
         // Tar fram analytiska lösningen------------------
         // std::string correctAnswer = "Text files/error files cos/t"+std::to_string(t)+"_e^cos_N"+std::to_string(num)+".0.txt";
-        // std::string correctAnswer = "Text files/error files x/t"+std::to_string(t)+"_x(10-x)_N"+std::to_string(num)+".0.txt";
+        // std::string correctAnswer = "Text files/files 10-x/t"+std::to_string(t)+"_N"+std::to_string(num)+".0.txt";
+        // std::string correctAnswer = "Text files/kopriva ex/Ans_t"+std::to_string(t)+"_N"+std::to_string(num)+".0.txt";
         std::string correctAnswer = "Text files/files cos2pi/t"+std::to_string(t)+"_N"+std::to_string(num)+".0.txt";
         std::vector<std::complex<float>> correctSolution = callFFT.getInput(correctAnswer,num);
 
         float max = 0;
+        float temp = 0;
         for(int j=0;j<num;j++)
         {
-            float temp = std::abs(correctSolution[j]-pdeSolution[j]);
-            if(max<=temp)
+            // temp += std::pow(correctSolution[j].real()-pdeSolution[j].real(),2);
+            temp=std::abs(correctSolution[j]-pdeSolution[j]);
+            if(temp>=max)
             {
                 max=temp;
             }
         }
+        // max = 2*PI*temp/static_cast<double>(i);
         infNorm.push_back(max);
     }
     // callFFT.printToFile(infNorm,"Text files/infNorm_e^cos_t"+std::to_string(t)+".txt",5);
-    // callFFT.printToFile(infNorm,"Text files/infNorm_x(10-x)_t"+std::to_string(t)+".txt",5);
-    callFFT.printToFile(infNorm,"Text files/2pi_infNorm_t"+std::to_string(t)+".txt",5);
+    // callFFT.printToFile(infNorm,"Text files/infNorm_x(10-x)_t"+std::to_string(t)+".txt",6);
+    callFFT.printToFile(infNorm,"Text files/2pi_infNorm_t"+std::to_string(t)+".txt",6);
+    // callFFT.printToFile(infNorm,"Text files/kopriva_2norm_t"+std::to_string(t)+".txt",6);
+    // callFFT.printToFile(infNorm,"Text files/kopriva_2norm_t2.txt",7);
     std::system("python Python\\ files/errorPlot.py");
 
 }
@@ -56,22 +65,24 @@ int main()
     // FFT callFFT;
     // int n = 16;
     // float T = 1;
-    // int NT = 500;
+    // int NT = 2000;
 
     // // v är konstanten i diffusion problemet, v=0 betyder advection problem-------------------
-    // float v = 0;
+    // float v = 0.3;
     // // c är konstanten i advektion problem
-    // float c = 5;
+    // float c = 1;
 
-    // // std::string inFile = "Text files/error files x/t0_x(10-x)_N16.0.txt";
-    // std::string inFile = "Text files/cos2pi.txt";
+    // // std::string inFile = "Text files/files x/t0_x(10-x)_N16.0.txt";
+    // // std::string inFile = "Text files/cos2pi.txt";
+    // std::string inFile = "Text files/phi.txt";
     // std::vector<std::complex<float>> f = callPDE.FourierCollocationDriver(n,NT,T,v,c,inFile);
-    // callFFT.printToFile(f,"Text files/svar.txt",n);
+    // callFFT.printToFile(f,"Text files/svar2.txt",n);
 
-    // // Startar python kod för att plot:a resultatet
+    // Startar python kod för att plot:a resultatet
     // std::system("python Python\\ files/pdePlot.py");
 
-    PDEerror();
+    // PDEerror();
+    std::system("python Python\\ files/errorPlot.py");
 
     return 0;
 }
diff --git a/Python files/GenerateData.py b/Python files/GenerateData.py
index 1c51bb9b7471f57c712881802e63246217631371..6fa388eb320c24ea0d22254ab13067d09525f81a 100644
--- a/Python files/GenerateData.py	
+++ b/Python files/GenerateData.py	
@@ -1,4 +1,5 @@
 import math
+import cmath
 
 # 3/(5-4cos())------------------------------------------------
 # filename = '../Text files/phi0.txt'
@@ -10,6 +11,32 @@ import math
 # file.close()
 # print('done')
 
+# numDataPoints = 16
+# intnum = int(numDataPoints)
+# filename = '../Text files/phi.txt'
+# file = open(filename, 'w')
+
+# file.close()
+# for l in range(1,9):
+#     numDataPoints = math.pow(2,l)
+#     strnum=str(numDataPoints)
+#     intnum = int(numDataPoints)
+#     filename = '../Text files/kopriva ex/phi_t0_N'+strnum+'.txt'
+#     time = 0
+#     file = open(filename, 'w')
+#     for i in range(intnum):
+#         k=i*2*math.pi/(intnum-1)
+#         z=0
+#         # for m in range(0,intnum):
+#         #     z+=math.pow(2,-m)*cmath.exp(1j*m*(k-time)-0.3*numDataPoints*math.pow(m,2))
+#         #     pass
+#         # file.write('('+str(z.real)+','+str(z.imag)+')'+'\n')    
+#         file.write(str(3/(5-4*math.cos(k))) + '\n')
+#     pass
+#     file.close()
+
+
+
 # 2cos(3x)-----------------------------------------------------
 # filename = '../Text files/sinus.txt'
 # numDataPoints = 33000
@@ -34,19 +61,21 @@ import math
 
 # cos------------------------------------------------
 
-for j in range(1,7):
+for j in range(1,9):
     numDataPoints = math.pow(2,j)
     strnum=str(numDataPoints)
     intnum = int(numDataPoints)
-    filename = '../Text files/files cos2pi/t2_N'+strnum+'.txt'
+    filename = '../Text files/files 10-x/t2_N'+strnum+'.txt'
     time = 2
     file = open(filename, 'w')
     for i in range(intnum):
-        j=i*2*math.pi/(intnum-1)
-        # if(j>=time):
-        file.write(str(math.exp(math.cos(j-time))) + '\n')
-        # else:
-        #     file.write(str(((j+10-time)*(10-(j+10-time)))) + '\n')
+        # j=i*2*math.pi/(intnum-1)
+        j=i*10/(intnum-1)
+        if(j>=time):
+        # file.write(str(math.exp(math.cos(j-time))) + '\n')
+            file.write(str((j-time)*(10-(j-time))) + '\n')
+        else:
+            file.write(str(((j+10-time)*(10-(j+10-time)))) + '\n')
 
         pass
     file.close()
diff --git a/Python files/errorPlot.py b/Python files/errorPlot.py
index 34b674094da68eef5e9eca3fb72e272ed30e7b1e..a74fa99a523813b31a2fcece342986c3d1299ce1 100644
--- a/Python files/errorPlot.py	
+++ b/Python files/errorPlot.py	
@@ -5,13 +5,19 @@ import math
 # filename0 = 'Text files/infNorm_e^cos_t1.txt'
 # filename1 = 'Text files/infNorm_e^cos_t2.txt'
 
-filename0 = 'Text files/infNorm_x(10-x)_t1.txt'
-filename1 = 'Text files/infNorm_x(10-x)_t2.txt'
+# filename0 = 'Text files/infNorm_x(10-x)_t1.txt'
+# filename1 = 'Text files/infNorm_x(10-x)_t2.txt'
+
 # filename0 = '../Text files/error files cos/t0_e^cos_N64.0.txt'
 # filename1 = '../Text files/error files cos/t2_e^cos_N64.0.txt'
+# filename0 = '../Text files/files x/t1_x(10-x)_N32.0.txt'
+# filename1 = '../Text files/files 10-x/t2_N32.0.txt'
+
+# filename0='Text files/2pi_infNorm_t1.txt'
+# filename1='Text files/2pi_infNorm_t2.txt'
 
-filename0='Text files/2pi_infNorm_t1.txt'
-filename1='Text files/2pi_infNorm_t2.txt'
+filename0 = 'Text files/kopriva_2norm_t1.txt'
+filename1='Text files/kopriva_2norm_t2.txt'
 
 X = []
 
@@ -25,12 +31,14 @@ Y1, imag= np.loadtxt(filename1, delimiter =',',unpack=True)
 
 for i in range(start,len(Y)+start):
     X.append(math.pow(2,i))
-    # X.append(i*10/(len(Y)-1))
     # X2.append(i*10/15)
     # X3.append(i*10/15)
 
+# for i in range(0,len(Y)):
+#         X.append(i*10/(len(Y)-1))
+
 
-plt.yscale('log', base=2)
+plt.yscale('log')
 plt.scatter(X, Y)
 plt.plot(X, Y, label = "t=1")
 
diff --git a/Python files/pdePlot.py b/Python files/pdePlot.py
index 9faaf87070ba1dbe6e302fb7a9d3acde78db0666..259505bd889ba3ea0c5f87dd83f8a28ed5d8e675 100644
--- a/Python files/pdePlot.py	
+++ b/Python files/pdePlot.py	
@@ -24,11 +24,12 @@ import math
 
 # -------------------------------------------------------------------
 # filename0 = 'Text files/x(2pi-x).txt'
-filename0 = 'Text files/error files x/t0_x(10-x)_N16.0.txt'
+filename0 = 'Text files/files x/t0_x(10-x)_N16.0.txt'
 filename1 = 'Text files/svar.txt'
-# filename2 = 'Text files/svar2.txt'
+filename2 = 'Text files/svar2.txt'
 
-filename0 = 'Text files/cos2pi.txt'
+# filename0 = 'Text files/cos2pi.txt'
+filename0 = 'Text files/phi.txt'
 
 X = []
 X1 = []
@@ -37,11 +38,11 @@ X3 = []
 
 Y = np.loadtxt(filename0, unpack=True,max_rows=16)
 Y1, imag= np.loadtxt(filename1, delimiter =',',unpack=True)
-# Y2, imag= np.loadtxt(filename2, delimiter =',',unpack=True)
+Y2, imag= np.loadtxt(filename2, delimiter =',',unpack=True)
 # Y3, imag= np.loadtxt(filename3, delimiter =',',unpack=True)
 for i in range(0,len(Y)):
-    X.append(i*2*math.pi/15)
-    X1.append(i*2*math.pi/15)
+    X.append(i*2/15)
+    X1.append(i*2/15)
     X2.append(i*10/15)
     X3.append(i*10/15)
 
@@ -50,11 +51,13 @@ for i in range(0,len(Y)):
 plt.scatter(X, Y)
 plt.plot(X, Y, label = "u(x,0)")
 
-plt.plot(X1, Y1, label = "u(x,5)",linestyle='--')
+
+plt.plot(X1, Y2, label = "u(x,1)",linestyle=':', color='k')
+plt.scatter(X1, Y2, color='k')
+
+plt.plot(X1, Y1, label = "u(x,2)",linestyle='--')
 plt.scatter(X1, Y1)
 
-# plt.plot(X2, Y2, label = "u(x,1)",linestyle='-', color='k')
-# plt.scatter(X2, Y2, color='k')
 
 # plt.plot(X3, Y3, label = "3",linestyle=':')
 # plt.scatter(X3, Y3)
diff --git a/Text files/2pi_infNorm_t1.txt b/Text files/2pi_infNorm_t1.txt
index b11f969bcfc494f12acec50f6b21315d5bfe56fa..6d0abb35ae2760a80424af1dd6bc1727ea9534e5 100644
--- a/Text files/2pi_infNorm_t1.txt	
+++ b/Text files/2pi_infNorm_t1.txt	
@@ -1,5 +1,6 @@
-1.4048632383,0.0000000000
-0.8443111181,0.0000000000
-0.5075711012,0.0000000000
-0.2478187084,0.0000000000
-0.1219187975,0.0000000000
+1.4048615694,0.0000000000
+0.8443094492,0.0000000000
+0.5075615644,0.0000000000
+0.2478169203,0.0000000000
+0.1219153404,0.0000000000
+0.0606518984,0.0000000000
diff --git a/Text files/2pi_infNorm_t2.txt b/Text files/2pi_infNorm_t2.txt
index 478bf82eeac71c776e44b19cb0b9603c6ea80346..67695e10fc1f086ab2c1c443d89333c610a89686 100644
--- a/Text files/2pi_infNorm_t2.txt	
+++ b/Text files/2pi_infNorm_t2.txt	
@@ -1,5 +1,6 @@
-1.5235233307,0.0000000000
-0.7697051764,0.0000000000
-0.4072552919,0.0000000000
-0.2010158300,0.0000000000
-0.0989584923,0.0000000000
+1.5235252380,0.0000000000
+0.7697018385,0.0000000000
+0.4072645903,0.0000000000
+0.2010155916,0.0000000000
+0.0989645720,0.0000000000
+0.0491771698,0.0000000000
diff --git a/Text files/files 10-x/t0_N128.0.txt b/Text files/files 10-x/t0_N128.0.txt
new file mode 100644
index 0000000000000000000000000000000000000000..c0032b9233670773ccaad9e4422aa847db1c0940
--- /dev/null
+++ b/Text files/files 10-x/t0_N128.0.txt	
@@ -0,0 +1,128 @@
+0.0
+0.7812015624031248
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diff --git a/Text files/files 10-x/t0_N16.0.txt b/Text files/files 10-x/t0_N16.0.txt
new file mode 100644
index 0000000000000000000000000000000000000000..74f3e3f51349ea9fc4b51a6708dc75c99618c78a
--- /dev/null
+++ b/Text files/files 10-x/t0_N16.0.txt	
@@ -0,0 +1,16 @@
+0.0
+6.222222222222222
+11.555555555555554
+16.0
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+22.22222222222222
+24.0
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diff --git a/Text files/files 10-x/t0_N2.0.txt b/Text files/files 10-x/t0_N2.0.txt
new file mode 100644
index 0000000000000000000000000000000000000000..21c4851a7c8d03439549b477be17c4622d31cb6f
--- /dev/null
+++ b/Text files/files 10-x/t0_N2.0.txt	
@@ -0,0 +1,2 @@
+0.0
+0.0
diff --git a/Text files/files 10-x/t0_N256.0.txt b/Text files/files 10-x/t0_N256.0.txt
new file mode 100644
index 0000000000000000000000000000000000000000..a2fc763da12e63d2108500b51ab23b16e913ea4c
--- /dev/null
+++ b/Text files/files 10-x/t0_N256.0.txt	
@@ -0,0 +1,256 @@
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