Khair Muhammad Saraz

again facing error kindly rectify it...

Answered: Khair Muhammad Saraz 40

May 23 2024

0 0

@acer

I'm having some trouble incorporating your code into another file. I've attached the file for your reference.

Download DQMSixth_(2).mw

The error graph is ploted correctly but I want you to please work on two key things I'd like to achieve:

Visualization: Ensure the theoretical results are displayed correctly and the 3D surface of approximate values should match the one for exact values that I already plotted in the file.
Comparison (Optional): If possible, I'd like to see a 2D graph that compares the exact values with the approximate values obtained from the code. However, the most important aspect is getting the approximate 3D surface to work as intended.

Appreciation...

Answered: Khair Muhammad Saraz 40

May 23 2024

0 0

@acer thank you for your heartly cooperation.

how to plot surface 3d in maple?...

Answered: Khair Muhammad Saraz 40

May 23 2024

0 0

@acer i want to plot surface 3d that is static , you have done very much smilar to that but i want 3d surface i am sending you the surface that is ploted in matlab i want to plot same using my calculated data in maple

How to generate 3D approximately surface...

Answered: Khair Muhammad Saraz 40

May 22 2024

0 0

@acer can you do that both? I want the solution as soos as possible thats why I'm asking questions again and again sorry for inconvenience. I don't want exact 3d graph for now i just want approximate 3d graph. Of pde solved by using dqm method.

dq_code_1.mw

i have given you the code kindly explain...

Answered: Khair Muhammad Saraz 40

May 22 2024

0 0

dq_code_(1).mw

>

(1)

>

(2)

>

localroots := fsolve(P_N = 0, x, complex)

(3)

>

for i to N do assign(x[i] = localroots[i]) end do

>

(4)

>

for i to N do for j to N do if i <> j then a[i, j] := (eval(PRime, x = x[i]))/((x[i]-x[j])*(eval(PRime, x = x[j]))) else a[i, j] := (1-2*x[i])/(2*x[i]*(x[i]-1)) end if end do end do

>	$u := proc (i) local u_x, expr, j; u_x := add(a[i, j]u[j], j = 1 .. N); expr := -u[i]u_x+x[i]; expr end proc; odes := [seq(u(i, [seq(u[j], j = 1 .. N)]), i = 1 .. N)]; for i to N do assign(o[i] = odes[i]) end do; for i to N do printf("u_%d = %s\n", i, convert(u(i), string)) end do$

u_1 = -u[1]*(-10.1340811913091*u[1]+15.4039041703445*u[2]-8.08708750877537*u[3]+3.92079823166652*u[4]-1.10353370192667*u[5])+.046910077030668
u_2 = -u[2]*(-1.92051204726391*u[1]-1.51670643433575*u[2]+4.80550130432862*u[3]-1.85711605328765*u[4]+.488833230558754*u[5])+.230765344947158
u_3 = -u[3]*(.602336319455661*u[1]-2.87077648466948*u[2]-1.11022302462516e-015*u[3]+2.87077648466942*u[4]-.602336319455684*u[5])+.5
u_4 = -u[4]*(-.488833230558737*u[1]+1.85711605328767*u[2]-4.8055013043286*u[3]+1.51670643433578*u[4]+1.92051204726404*u[5])+.769234655052844
u_5 = -u[5]*(1.1035337019266*u[1]-3.92079823166643*u[2]+8.08708750877511*u[3]-15.4039041703442*u[4]+10.1340811913086*u[5])+.95308992296933

>

>	$for i to N do printf("Initial condition for u_%d: u_%d(0) = %f\n", i, i, initial_conditions[i]) end do$

Initial condition for u_1: u_1(0) = 0.010000
Initial condition for u_2: u_2(0) = 0.020000
Initial condition for u_3: u_3(0) = 0.030000
Initial condition for u_4: u_4(0) = 0.040000
Initial condition for u_5: u_5(0) = 0.050000

>

for i to N do o_old[i] := initial_conditions[i] end do

>

_local(time); time := 0.

(5)

>

Old value for u_1: 0.010000, New value for u_1: 0.014546
Absolute error for u_1 at time 0.000000: 0.004546
Old value for u_2: 0.020000, New value for u_2: 0.042761
Absolute error for u_2 at time 0.000000: 0.022761
Old value for u_3: 0.030000, New value for u_3: 0.079503
Absolute error for u_3 at time 0.000000: 0.049503
Old value for u_4: 0.040000, New value for u_4: 0.116125
Absolute error for u_4 at time 0.000000: 0.076125
Old value for u_5: 0.050000, New value for u_5: 0.144117
Absolute error for u_5 at time 0.000000: 0.094117

Old value for u_1: 0.014546, New value for u_1: 0.018877
Absolute error for u_1 at time 0.100000: 0.004332
Old value for u_2: 0.042761, New value for u_2: 0.064782
Absolute error for u_2 at time 0.100000: 0.022021
Old value for u_3: 0.079503, New value for u_3: 0.127586
Absolute error for u_3 at time 0.100000: 0.048082
Old value for u_4: 0.116125, New value for u_4: 0.190060
Absolute error for u_4 at time 0.100000: 0.073936
Old value for u_5: 0.144117, New value for u_5: 0.235364
Absolute error for u_5 at time 0.100000: 0.091247

Old value for u_1: 0.018877, New value for u_1: 0.022924
Absolute error for u_1 at time 0.200000: 0.004047
Old value for u_2: 0.064782, New value for u_2: 0.085678
Absolute error for u_2 at time 0.200000: 0.020896
Old value for u_3: 0.127586, New value for u_3: 0.173392
Absolute error for u_3 at time 0.200000: 0.045807
Old value for u_4: 0.190060, New value for u_4: 0.260525
Absolute error for u_4 at time 0.200000: 0.070465
Old value for u_5: 0.235364, New value for u_5: 0.322219
Absolute error for u_5 at time 0.200000: 0.086855

Old value for u_1: 0.022924, New value for u_1: 0.026635
Absolute error for u_1 at time 0.300000: 0.003711
Old value for u_2: 0.085678, New value for u_2: 0.105142
Absolute error for u_2 at time 0.300000: 0.019463
Old value for u_3: 0.173392, New value for u_3: 0.216230
Absolute error for u_3 at time 0.300000: 0.042837
Old value for u_4: 0.260525, New value for u_4: 0.326485
Absolute error for u_4 at time 0.300000: 0.065960
Old value for u_5: 0.322219, New value for u_5: 0.403474
Absolute error for u_5 at time 0.300000: 0.081256

Old value for u_1: 0.026635, New value for u_1: 0.029977
Absolute error for u_1 at time 0.400000: 0.003342
Old value for u_2: 0.105142, New value for u_2: 0.122956
Absolute error for u_2 at time 0.400000: 0.017814
Old value for u_3: 0.216230, New value for u_3: 0.255595
Absolute error for u_3 at time 0.400000: 0.039366
Old value for u_4: 0.326485, New value for u_4: 0.387191
Absolute error for u_4 at time 0.400000: 0.060706
Old value for u_5: 0.403474, New value for u_5: 0.478270
Absolute error for u_5 at time 0.400000: 0.074796

Old value for u_1: 0.029977, New value for u_1: 0.032937
Absolute error for u_1 at time 0.500000: 0.002960
Old value for u_2: 0.122956, New value for u_2: 0.139000
Absolute error for u_2 at time 0.500000: 0.016044
Old value for u_3: 0.255595, New value for u_3: 0.291189
Absolute error for u_3 at time 0.500000: 0.035593
Old value for u_4: 0.387191, New value for u_4: 0.442190
Absolute error for u_4 at time 0.500000: 0.054999
Old value for u_5: 0.478270, New value for u_5: 0.546091
Absolute error for u_5 at time 0.500000: 0.067820

Old value for u_1: 0.032937, New value for u_1: 0.035518
Absolute error for u_1 at time 0.600000: 0.002581
Old value for u_2: 0.139000, New value for u_2: 0.153237
Absolute error for u_2 at time 0.600000: 0.014238
Old value for u_3: 0.291189, New value for u_3: 0.322898
Absolute error for u_3 at time 0.600000: 0.031709
Old value for u_4: 0.442190, New value for u_4: 0.491302
Absolute error for u_4 at time 0.600000: 0.049113
Old value for u_5: 0.546091, New value for u_5: 0.606735
Absolute error for u_5 at time 0.600000: 0.060644

Old value for u_1: 0.035518, New value for u_1: 0.037738
Absolute error for u_1 at time 0.700000: 0.002219
Old value for u_2: 0.153237, New value for u_2: 0.165707
Absolute error for u_2 at time 0.700000: 0.012470
Old value for u_3: 0.322898, New value for u_3: 0.350773
Absolute error for u_3 at time 0.700000: 0.027875
Old value for u_4: 0.491302, New value for u_4: 0.534585
Absolute error for u_4 at time 0.700000: 0.043283
Old value for u_5: 0.606735, New value for u_5: 0.660273
Absolute error for u_5 at time 0.700000: 0.053538

Old value for u_1: 0.037738, New value for u_1: 0.039621
Absolute error for u_1 at time 0.800000: 0.001884
Old value for u_2: 0.165707, New value for u_2: 0.176501
Absolute error for u_2 at time 0.800000: 0.010794
Old value for u_3: 0.350773, New value for u_3: 0.374988
Absolute error for u_3 at time 0.800000: 0.024215
Old value for u_4: 0.534585, New value for u_4: 0.572283
Absolute error for u_4 at time 0.800000: 0.037697
Old value for u_5: 0.660273, New value for u_5: 0.706991
Absolute error for u_5 at time 0.800000: 0.046718

Old value for u_1: 0.039621, New value for u_1: 0.041201
Absolute error for u_1 at time 0.900000: 0.001580
Old value for u_2: 0.176501, New value for u_2: 0.185750
Absolute error for u_2 at time 0.900000: 0.009249
Old value for u_3: 0.374988, New value for u_3: 0.395806
Absolute error for u_3 at time 0.900000: 0.020818
Old value for u_4: 0.572283, New value for u_4: 0.604773
Absolute error for u_4 at time 0.900000: 0.032490
Old value for u_5: 0.706991, New value for u_5: 0.747334
Absolute error for u_5 at time 0.900000: 0.040343

Final value for u_1: u_1(tf) = 0.041201
Final value for u_2: u_2(tf) = 0.185750
Final value for u_3: u_3(tf) = 0.395806
Final value for u_4: u_4(tf) = 0.604773
Final value for u_5: u_5(tf) = 0.747334

>

Download dq_code_(1).mw

@mmcdara

how to generate graph of iterated values...

Answered: Khair Muhammad Saraz 40

May 22 2024

0 0

@acer i am attaching the maple code kindly modify it as soon as possible i will be very thank full i want to plot 3d graph of my result . i have converted pde into system of odes using differential quadrature method and after that i have solved it through using rk4 method now i want to use all those values generating from system of odes as x values and time from 0 to 1 to make 3d plot but unable to do that

>

(1)

>

(2)

>

localroots := fsolve(P_N = 0, x, complex)

(3)

>

for i to N do assign(x[i] = localroots[i]) end do

>

(4)

>

for i to N do for j to N do if i <> j then a[i, j] := (eval(PRime, x = x[i]))/((x[i]-x[j])*(eval(PRime, x = x[j]))) else a[i, j] := (1-2*x[i])/(2*x[i]*(x[i]-1)) end if end do end do

>	$u := proc (i) local u_x, expr, j; u_x := add(a[i, j]u[j], j = 1 .. N); expr := -u[i]u_x+x[i]; expr end proc; odes := [seq(u(i, [seq(u[j], j = 1 .. N)]), i = 1 .. N)]; for i to N do assign(o[i] = odes[i]) end do; for i to N do printf("u_%d = %s\n", i, convert(u(i), string)) end do$

u_1 = -u[1]*(-10.1340811913091*u[1]+15.4039041703445*u[2]-8.08708750877537*u[3]+3.92079823166652*u[4]-1.10353370192667*u[5])+.046910077030668
u_2 = -u[2]*(-1.92051204726391*u[1]-1.51670643433575*u[2]+4.80550130432862*u[3]-1.85711605328765*u[4]+.488833230558754*u[5])+.230765344947158
u_3 = -u[3]*(.602336319455661*u[1]-2.87077648466948*u[2]-1.11022302462516e-015*u[3]+2.87077648466942*u[4]-.602336319455684*u[5])+.5
u_4 = -u[4]*(-.488833230558737*u[1]+1.85711605328767*u[2]-4.8055013043286*u[3]+1.51670643433578*u[4]+1.92051204726404*u[5])+.769234655052844
u_5 = -u[5]*(1.1035337019266*u[1]-3.92079823166643*u[2]+8.08708750877511*u[3]-15.4039041703442*u[4]+10.1340811913086*u[5])+.95308992296933

>

>	$for i to N do printf("Initial condition for u_%d: u_%d(0) = %f\n", i, i, initial_conditions[i]) end do$

Initial condition for u_1: u_1(0) = 0.010000
Initial condition for u_2: u_2(0) = 0.020000
Initial condition for u_3: u_3(0) = 0.030000
Initial condition for u_4: u_4(0) = 0.040000
Initial condition for u_5: u_5(0) = 0.050000

>

for i to N do o_old[i] := initial_conditions[i] end do

>

_local(time); time := 0.

(5)

>

Old value for u_1: 0.010000, New value for u_1: 0.014546
Absolute error for u_1 at time 0.000000: 0.004546
Old value for u_2: 0.020000, New value for u_2: 0.042761
Absolute error for u_2 at time 0.000000: 0.022761
Old value for u_3: 0.030000, New value for u_3: 0.079503
Absolute error for u_3 at time 0.000000: 0.049503
Old value for u_4: 0.040000, New value for u_4: 0.116125
Absolute error for u_4 at time 0.000000: 0.076125
Old value for u_5: 0.050000, New value for u_5: 0.144117
Absolute error for u_5 at time 0.000000: 0.094117

Old value for u_1: 0.014546, New value for u_1: 0.018877
Absolute error for u_1 at time 0.100000: 0.004332
Old value for u_2: 0.042761, New value for u_2: 0.064782
Absolute error for u_2 at time 0.100000: 0.022021
Old value for u_3: 0.079503, New value for u_3: 0.127586
Absolute error for u_3 at time 0.100000: 0.048082
Old value for u_4: 0.116125, New value for u_4: 0.190060
Absolute error for u_4 at time 0.100000: 0.073936
Old value for u_5: 0.144117, New value for u_5: 0.235364
Absolute error for u_5 at time 0.100000: 0.091247

Old value for u_1: 0.018877, New value for u_1: 0.022924
Absolute error for u_1 at time 0.200000: 0.004047
Old value for u_2: 0.064782, New value for u_2: 0.085678
Absolute error for u_2 at time 0.200000: 0.020896
Old value for u_3: 0.127586, New value for u_3: 0.173392
Absolute error for u_3 at time 0.200000: 0.045807
Old value for u_4: 0.190060, New value for u_4: 0.260525
Absolute error for u_4 at time 0.200000: 0.070465
Old value for u_5: 0.235364, New value for u_5: 0.322219
Absolute error for u_5 at time 0.200000: 0.086855

Old value for u_1: 0.022924, New value for u_1: 0.026635
Absolute error for u_1 at time 0.300000: 0.003711
Old value for u_2: 0.085678, New value for u_2: 0.105142
Absolute error for u_2 at time 0.300000: 0.019463
Old value for u_3: 0.173392, New value for u_3: 0.216230
Absolute error for u_3 at time 0.300000: 0.042837
Old value for u_4: 0.260525, New value for u_4: 0.326485
Absolute error for u_4 at time 0.300000: 0.065960
Old value for u_5: 0.322219, New value for u_5: 0.403474
Absolute error for u_5 at time 0.300000: 0.081256

Old value for u_1: 0.026635, New value for u_1: 0.029977
Absolute error for u_1 at time 0.400000: 0.003342
Old value for u_2: 0.105142, New value for u_2: 0.122956
Absolute error for u_2 at time 0.400000: 0.017814
Old value for u_3: 0.216230, New value for u_3: 0.255595
Absolute error for u_3 at time 0.400000: 0.039366
Old value for u_4: 0.326485, New value for u_4: 0.387191
Absolute error for u_4 at time 0.400000: 0.060706
Old value for u_5: 0.403474, New value for u_5: 0.478270
Absolute error for u_5 at time 0.400000: 0.074796

Old value for u_1: 0.029977, New value for u_1: 0.032937
Absolute error for u_1 at time 0.500000: 0.002960
Old value for u_2: 0.122956, New value for u_2: 0.139000
Absolute error for u_2 at time 0.500000: 0.016044
Old value for u_3: 0.255595, New value for u_3: 0.291189
Absolute error for u_3 at time 0.500000: 0.035593
Old value for u_4: 0.387191, New value for u_4: 0.442190
Absolute error for u_4 at time 0.500000: 0.054999
Old value for u_5: 0.478270, New value for u_5: 0.546091
Absolute error for u_5 at time 0.500000: 0.067820

Old value for u_1: 0.032937, New value for u_1: 0.035518
Absolute error for u_1 at time 0.600000: 0.002581
Old value for u_2: 0.139000, New value for u_2: 0.153237
Absolute error for u_2 at time 0.600000: 0.014238
Old value for u_3: 0.291189, New value for u_3: 0.322898
Absolute error for u_3 at time 0.600000: 0.031709
Old value for u_4: 0.442190, New value for u_4: 0.491302
Absolute error for u_4 at time 0.600000: 0.049113
Old value for u_5: 0.546091, New value for u_5: 0.606735
Absolute error for u_5 at time 0.600000: 0.060644

Old value for u_1: 0.035518, New value for u_1: 0.037738
Absolute error for u_1 at time 0.700000: 0.002219
Old value for u_2: 0.153237, New value for u_2: 0.165707
Absolute error for u_2 at time 0.700000: 0.012470
Old value for u_3: 0.322898, New value for u_3: 0.350773
Absolute error for u_3 at time 0.700000: 0.027875
Old value for u_4: 0.491302, New value for u_4: 0.534585
Absolute error for u_4 at time 0.700000: 0.043283
Old value for u_5: 0.606735, New value for u_5: 0.660273
Absolute error for u_5 at time 0.700000: 0.053538

Old value for u_1: 0.037738, New value for u_1: 0.039621
Absolute error for u_1 at time 0.800000: 0.001884
Old value for u_2: 0.165707, New value for u_2: 0.176501
Absolute error for u_2 at time 0.800000: 0.010794
Old value for u_3: 0.350773, New value for u_3: 0.374988
Absolute error for u_3 at time 0.800000: 0.024215
Old value for u_4: 0.534585, New value for u_4: 0.572283
Absolute error for u_4 at time 0.800000: 0.037697
Old value for u_5: 0.660273, New value for u_5: 0.706991
Absolute error for u_5 at time 0.800000: 0.046718

Old value for u_1: 0.039621, New value for u_1: 0.041201
Absolute error for u_1 at time 0.900000: 0.001580
Old value for u_2: 0.176501, New value for u_2: 0.185750
Absolute error for u_2 at time 0.900000: 0.009249
Old value for u_3: 0.374988, New value for u_3: 0.395806
Absolute error for u_3 at time 0.900000: 0.020818
Old value for u_4: 0.572283, New value for u_4: 0.604773
Absolute error for u_4 at time 0.900000: 0.032490
Old value for u_5: 0.706991, New value for u_5: 0.747334
Absolute error for u_5 at time 0.900000: 0.040343

Final value for u_1: u_1(tf) = 0.041201
Final value for u_2: u_2(tf) = 0.185750
Final value for u_3: u_3(tf) = 0.395806
Final value for u_4: u_4(tf) = 0.604773
Final value for u_5: u_5(tf) = 0.747334

>

Download dq_code_(1).mw

how to make graph with the numerical val...

Answered: Khair Muhammad Saraz 40

May 22 2024

0 0

@dharr i want to make 3d plot of approximate values can you help me with that?

how to generate graph with functions hav...

Answered: Khair Muhammad Saraz 40

May 22 2024

0 0

@mmcdara i have numbers that i have generated from an iterated method now i want to use those numbers with time interval to make 3d graph. what i mean to say is this I dont have specific ruIe to define function with variables i just have numbers.

differential quadrature...

Answered: Khair Muhammad Saraz 40

May 21 2024

0 0

i have corrected above code now im just stuck with the graphs can you help me with that?i want to generate graph of exact solution , approximate solution and error

Download DQMSixth.mw