[NA] Added initial solution

1 files changed, 78 insertions, 0 deletions

diff --git a/Year 3/Numerical analysis/Project.wl b/Year 3/Numerical analysis/Project.wl
new file mode 100644
index 0000000..9948423
--- /dev/null
+++ b/Year 3/Numerical analysis/Project.wl
@@ -0,0 +1,78 @@
+(*----------
+* 1 задача
+*----------*)
+ApproxIntegral[M_,a_,b_,f_]:= With[
+  {
+    h=(b-a)/(2M),
+    xk=Function[k,a+k*(b-a)/(2M)]
+  },
+  (h/3)(f[a]+f[b]) +
+  (2h/3)Sum[f[xk[2k]],{k,1,M-1}]+
+  (4h/3)Sum[f[xk[2k-1]],{k,1,M}]
+]
+
+Integrand[x_]:=1/((1+2x^2)^5)
+m15:=N[ApproxIntegral[15,-1,1,Integrand],{Infinity,20}]
+m50:=N[ApproxIntegral[50,-1,1,Integrand],{Infinity,20}]
+correct := N[Integrate[Integrand[x],{x,-1,1}],{Infinity,20}]
+
+Print["1 задача)"]
+Print["При M=15:        ",m15]
+Print["Разлика с точен: ", N[Abs[m15-correct],{Infinity,20}]]
+Print["При M=50:        ",m50]
+Print["Разлика с точен: ", N[Abs[m50-correct],{Infinity,20}]]
+
+(*----------
+* 2 задача
+*----------*)
+
+(* Намиране Pn *)
+Pncoeff [xs_,f_]:= With[
+  {
+    k=Length[xs],
+    x0=First[xs],
+    xk=Last[xs]
+  },
+  Piecewise[{
+    {
+      f[xk],
+      k==1
+    },
+    {
+      (Pncoeff[Drop[xs,1],f]-Pncoeff[Drop[xs,-1],f])/(xk-x0),
+      x0!=xk
+    },
+    {
+      D[f,{x,k}][x0]/((k-1)!),
+      x0==xk
+    }}]
+]
+
+Pn[f_,xsWithDup_]:=With[
+  { xs = DeleteDuplicates[xsWithDup] },
+  Function[x,Sum[
+    Pncoeff[Take[xs,i],f]*
+    Product[x-xs[[j]],{j,1,i-1}],
+    {i,1,Length[xs]}
+  ]]
+]
+
+f[x_]:=Piecewise[{
+  {Cos[3x],x<=Pi},
+  {x-Pi-1,x>Pi}
+}]
+values:={9Pi/10,10Pi/11,11Pi/10}
+newtonpolyn:=Pn[f,values]
+
+Collect[FullSimplify[InterpolatingPolynomial[{
+  {9Pi/10,f[9Pi/10]},
+  {10Pi/11,f[10Pi/11]},
+  {11Pi/10,f[11Pi/10]}
+},x]],x]
+
+Print["2 задача)"]
+Print["Полином: ",Collect[FullSimplify[newtonpolyn[x]],x]]
+
+(* Графика разлика *)
+Print["Графика на разлика:"]
+Plot[Abs[f[z]-newtonpolyn[z]],{z,-2Pi,2Pi}]