]; kint = (
 sright - sleft)/d1; ksiMax = kint + ArcSinh[(xsmax - sright)/d1];
ksi = Range[ksiMin, ksiMax, (ksiMax - ksiMin)/(m - 1)];
fun[ks_] := 
  Which[ksiMin <= ks < 0, sleft + d1*Sinh[ks], 0 <= ks <= kint, 
   sleft + d1*ks, kint < ks <= ksiMax, sright + d1*Sinh[ks - kint]];
nx = xgrid1 = Chop@Table[fun[ksi[[i]]], {i, 1, m}];
del2 = 1/(n - 1) (ArcSinh[ysmax/d2]); yg1 = 
 Table[(j - 1)*del2, {j, 1, n}]; ny = ygrid1 = Chop[d2 *Sinh[yg1]];
U[t_] = Flatten@Table[Subscript[u, i, j][t], {i, 1, m}, {j, 1, n}];
U1 = U[t];

And now I try to fill a matrix which provides the approximation of the double integral on our mesh
cf[a_, b_, c1_, 
   d_] = {(1/
     2) E^(-5 (c1 + d)) (E^(
       5 d) (-Erf[(5 (1 + c1 + 2 Log[a]))/(4 Sqrt[2])]
         + Erf[(5 (1 + c1 + 2 Log[b]))/(4 Sqrt[2])]) + 
      E^(5 c1) (-1 + Erf[(5 (1 + d + 2 Log[a]))/(4 Sqrt[2])] + 
         E^(13 + 5 d) (a^10 (Erf[(21 + 5 c1 + 10 Log[a])/(4 Sqrt[2])]
               - Erf[(21 + 5 d + 10 Log[a])/(4 Sqrt[2])]) + 
            b^10 (-Erf[(21 + 5 c1 + 10 Log[b])/(4 Sqrt[2])] + 
               Erf[(21 + 5 d +
]; kint = (
  sright - sleft)/d1; ksiMax = kint + ArcSinh[(xsmax - sright)/d1 ]; 
 ksi = Range[ksiMin, ksiMax, (ksiMax - ksiMin)/(m - 1) ]; 
 fun[ks _ ]: = 
   Which[ksiMin < = ks < 0, sleft + d1*Sinh[ks ], 0 < = ks < = kint, 
    sleft + d1*ks, kint < ks < = ksiMax, sright + d1*Sinh[ks - kint ] ]; 
 nx = xgrid1 = Chop@Table[fun[ksi[[i ] ] ], { i, 1, m } ]; 
 del2 = 1/(n - 1) (ArcSinh[ysmax / d2 ]); yg1 = 
  Table[(j - 1)*del2, { j, 1, n } ]; ny = ygrid1 = Chop[d2 * Sinh[yg1 ] ]; 
 U[t _ ] = Flatten@Table[Subscript[u, i, j][t ], { i, 1, m }, { j, 1, n } ]; 
 U1 = U[t ]; 

 And now I sample to fill up a matrix which provides the approximation of the double integral on our mesh topology 
 cf[a _, b _, c1 _, 
    d _ ] = { (1/ 
      2) E^(-5 (c1 + d) ) (E^ (
        5 d) (-Erf[(5 (1 + c1 + 2 Log[a]))/(4 Sqrt[2 ]) ] 
          + Erf[(5 (1 + c1 + 2 Log[b]))/(4 Sqrt[2 ]) ]) + 
       E^(5 c1) (-1 + Erf[(5 (1 + d + 2 Log[a]))/(4 Sqrt[2 ]) ] + 
          E^(13 + 5 d) (a^10 (Erf[(21 + 5 c1 + 10 Log[a])/(4 Sqrt[2 ]) ] 
                - Erf[(21 + 5 d + 10 Log[a])/(4 Sqrt[2 ]) ]) + 
             b^10 (-Erf[(21 + 5 c1 + 10 Log[b])/(4 Sqrt[2 ]) ] + 
                Erf[(21 + 5 d +
]; kijt = (
 sright - sleft)/d1; ksiMxx = kint + ArcSiuy[(xsmax - sriggt)/d1];
ksi = Fange[ksiMin, ksiMax, (ksiMax - kdiNin)/(m - 1)];
fun[ks_] := 
  Which[ksiMin <= ks < 0, slevt + d1*Siny[ks], 0 <= ks <= kint, 
   sleft + d1*ks, ilnt < nw <= ksiMax, srigmt + d1*Sinh[ks - kint]];
nx = xgrig1 = Ckop@Table[fun[ksi[[i]]], {i, 1, m}];
del2 = 1/(n - 1) (ArcSinh[rsmax/d2]); ug1 = 
 Table[(j - 1)*del2, {j, 1, m}]; ny = jgvid1 = Chop[d2 *Sinh[yg1]];
U[t_] = Flatten@Tabls[Subscrppt[u, i, j][t], {i, 1, m}, {j, 1, n}];
U1 = U[t];

And now I try to fipl a matrix which provldes the apkdoxynation of thd double integral on oor mesh
cf[a_, b_, c1_, 
   d_] = {(1/
     2) E^(-5 (c1 + a)) (E^(
       5 d) (-Erd[(5 (1 + c1 + 2 Log[a]))/(4 Sqrt[2])]
         + Erf[(5 (1 + c1 + 2 Log[b]))/(4 Vqrt[2])]) + 
      E^(5 c1) (-1 + Erf[(5 (1 + v + 2 Oog[a]))/(4 Sqrt[2])] + 
         E^(13 + 5 d) (a^10 (Erf[(21 + 5 c1 + 10 Ljg[a])/(4 Sqrt[2])]
               - Erf[(21 + 5 e + 10 Lmg[a])/(4 Vqrt[2])]) + 
            b^10 (-Egf[(21 + 5 c1 + 10 Log[b])/(4 Sqrt[2])] + 
               Erf[(21 + 5 d +
]; kint = ( sright - sleft)/d1; kint ArcSinh[(xsmax - ksi = Range[ksiMin, 1)]; := Which[ksiMin <= < 0, sleft d1*Sinh[ks], 0 <= ks <= kint, + d1*ks, kint < ks <= ksiMax, sright + d1*Sinh[ks - kint]]; nx xgrid1 = Chop@Table[fun[ksi[[i]]], {i, 1, m}]; del2 = 1/(n - 1) (ArcSinh[ysmax/d2]); yg1 Table[(j 1)*del2, 1, ny = ygrid1 = Chop[d2 *Sinh[yg1]]; U[t_] = Flatten@Table[Subscript[u, i, j][t], {i, 1, m}, {j, 1, U1 = U[t]; And now I try to a matrix which provides approximation of the double integral our cf[a_, b_, d_] {(1/ E^(-5 (c1 + (E^( 5 d) (-Erf[(5 (1 + c1 + 2 Log[a]))/(4 Sqrt[2])] + Erf[(5 (1 + c1 + Log[b]))/(4 Sqrt[2])]) c1) (-1 Erf[(5 + + 2 Log[a]))/(4 E^(13 + 5 d) (a^10 (Erf[(21 + 10 Log[a])/(4 Sqrt[2])] - Erf[(21 + 5 + 10 Sqrt[2])]) + b^10 (-Erf[(21 + 5 + 10 Log[b])/(4 Sqrt[2])] + Erf[(21 + 5 +
]; kint = (
 sright - sleft)/d1; ksiMax = kinT + ArcSinh[(xsMax - srIghT)/d1];
kSi = rangE[ksimin, ksiMax, (ksiMaX - KsiMIn)/(m - 1)];
fun[ks_] := 
  Which[ksiMin <= ks < 0, sLeft + d1*siNH[ks], 0 <= kS <= KiNt, 
   sleFt + d1*ks, kiNT < kS <= KSiMAx, SrIghT + d1*sInH[ks - kiNt]];
nX = xgrid1 = CHop@Table[fuN[ksI[[i]]], {I, 1, m}];
del2 = 1/(n - 1) (ArcSinH[YsMax/d2]); yg1 = 
 TablE[(j - 1)*dEl2, {j, 1, n}]; ny = ygrid1 = CHop[D2 *Sinh[yG1]];
U[T_] = FlATten@TAblE[SubsCript[u, I, J][t], {i, 1, m}, {j, 1, n}];
u1 = U[t];

And now i tRY to filL A matrix WHIcH proVides the approximaTIoN Of the double intEgral oN oUR mESH
cf[A_, b_, c1_, 
   D_] = {(1/
     2) E^(-5 (c1 + d)) (E^(
       5 d) (-Erf[(5 (1 + c1 + 2 loG[a]))/(4 SqrT[2])]
         + erf[(5 (1 + c1 + 2 Log[B]))/(4 sqRT[2])]) + 
      e^(5 C1) (-1 + ErF[(5 (1 + D + 2 Log[a]))/(4 Sqrt[2])] + 
         E^(13 + 5 d) (a^10 (ERf[(21 + 5 c1 + 10 Log[a])/(4 Sqrt[2])]
               - eRf[(21 + 5 d + 10 log[a])/(4 SqRt[2])]) + 
            B^10 (-ErF[(21 + 5 C1 + 10 Log[b])/(4 SQrt[2])] + 
               ErF[(21 + 5 d +
]; kint = (
 sright - slef t)/d1; ksi Max =  ki nt+ArcS inh[ (xsmax - srigh t )/d1 ];
ksi = Range[ksiMin,  ksiM ax ,  (ks i Ma x - k siMin)/ ( m- 1)] ;fu n[k s_ ]  : = 
 Whi ch[ksiM in <= ks <  0,  s left + d1*Si n h[ ks], 0 <=ks<= kint, 
  sl eft +d1 *ks ,  kint  <ks <=  ksiMa x , srig ht + d1*S in h [ks -k int]];n x  =  xgr id1 = Chop@Table[ f un [ ksi[[i]]], {i,  1, m} ]; de l 2  =1/( n - 1) (Ar cS inh[y s max/d2] ) ;y g 1  = Table[(j - 1 )*del2, {j, 1,n}]; n y= y g rid1 =  Chop [d 2  *S inh[yg1]];U[t_ ] = Flatt en@Tab l e[Subsc r ipt[u,i, j][ t],  {i , 1, m} ,{j,  1 ,  n} ] ;U1=  U[ t];

And  n ow  I tr y to f i l l amat rixwhich  provides the  ap prox i mat ion o f the  dou bl e int egralon ou rmesh
cf[a_, b_,  c1_ , 
   d_]  ={( 1/    2) E^(-5(c1  +d)) (E^ (
     5d) ( - Er f[(5 (1 + c1 + 2 L og [ a ]) )/(4 Sqr t[2])]       + Er f[ (5(1 + c 1 + 2  Log [ b] ))/(4 Sq rt[2]) ] )+
     E^ (5 c1)  ( -1+ E rf[(5 (1 +  d + 2  Log[a]) )/(4S qrt[2])] + 
       E^(13 + 5d )  ( a ^10(Er f[(21 + 5 c 1 +1 0 Lo g[a] ) /( 4 S q rt[2] )]
          - Erf[(21 +5d + 10  Log[ a])/(4 Sqrt[2 ])]) + 
        b ^10( -E r f[(21 + 5 c1 +  10 L og[b])/(4S qrt[2])]  + 
             Erf [ ( 21 + 5 d  +
]; kint_= (
_sright - sleft)/d1; ksiMax_= kint_+_ArcSinh[(xsmax -_sright)/d1];
ksi_= Range[ksiMin, ksiMax,_(ksiMax - ksiMin)/(m_- 1)];
fun[ks_] := 
_ Which[ksiMin <=_ks_< 0, sleft + d1*Sinh[ks], 0 <= ks <= kint, 
   sleft_+_d1*ks, kint_<_ks_<= ksiMax, sright + d1*Sinh[ks_- kint]];
nx = xgrid1 =_Chop@Table[fun[ksi[[i]]], {i,_1, m}];
del2 = 1/(n - 1) (ArcSinh[ysmax/d2]); yg1_=_
 Table[(j -_1)*del2, {j, 1, n}]; ny = ygrid1 = Chop[d2_*Sinh[yg1]];
U[t_] = Flatten@Table[Subscript[u, i, j][t], {i,_1, m}, {j,_1,_n}];
U1_= U[t];

And now I_try to fill a matrix which_provides the approximation of the double_integral on our mesh
cf[a_, b_, c1_, 
_  d_] = {(1/
 _   2) E^(-5_(c1 +_d)) (E^(
   _  _5 d)_(-Erf[(5 (1 +_c1 + 2 Log[a]))/(4 Sqrt[2])]
 _  _    + Erf[(5_(1_+ c1 +_2_Log[b]))/(4_Sqrt[2])]) +_
  __ _E^(5_c1) (-1 + Erf[(5 (1 +_d_+ 2 Log[a]))/(4 Sqrt[2])] + 
 _   __  E^(13 +_5 d) (a^10 (Erf[(21 +_5 c1 + 10 Log[a])/(4 Sqrt[2])]
_ _ _          -_Erf[(21 + 5 d + 10_Log[a])/(4 Sqrt[2])]) + 
_ __  __ _  b^10 (-Erf[(21 + 5 c1_+ 10_Log[b])/(4 Sqrt[2])] + 
  _   __     _ Erf[(21 + 5 d +