how can i solve this error , predictor corrector method

hey all

im trying to solve 2nd ode with RK4 and predictor corrector method , and i;m still receving this error ,what should i do?

clear all;
close all;
clc;


h=0.1;          %step size (changable according to the proplem)
x=0:h:1; %the X domain range
yic = [[1;-2],zeros(2, length(x)-1)]; %intial condition in form of matrix
                                      %(changable according to the proplem)
%*********************************************
%             Exact solution
%*********************************************
y_exact=exp(-2*x); %define your equation for exact solution
%**********************************************

%********* Numerical solution *****************
%% RK4th order definition 
for i = 1:3
        K11 = fn(x(i), yic(:, i));
        K12 = fn(x(i) + h/2, yic(:, i) + h*K11/2);
        K21 = fn(x(i) + h/2, yic(:, i) + h*K12/2);
        K22 = fn(x(i) + h,   yic(:, i) + h*K21);
        yic(:,i+1) = yic(:, i) + h/6*(K11 + 2*K12 + 2*K21 + K22);
end   
%%predictor corrector equation defenition
 for i = 5:11
        y_star=yic(:,i) + (h/24)*((55*fn(x(i),yic(:,i)))-(59*fn(x(i-1),yic(:,i-1))) +(37*fn(x(i-2),yic(:,i-2))) - (9*fn(x(i-3),yic(:,i-3))));
        yic(:,i+1) = yic(:,i)+(h/24)*((9*fn(x(i),y_star(:,i)))+(19*fn(x(i),yic(:,i)))-(5*fn(x(i-1),yic(:,i-1)))+(fn(x(i-3),yic(:,i-3))));
 end

%% print the output in the form of table
out=[x' y_exact' yic(1,:)'];
fprintf(' ------------------------------------------------\n')
fprintf('|   X    |  Y(exact)   |  Y(approximate))   |\n')
fprintf(' ------------------------------------------------\n')
fprintf('|  %3.1f   |  %3.6f   |     %3.6f       |\n',out')
fprintf(' ------------------------------------------------\n')
%% plotting the grapgh
plot(x, yic(1,:), 'r*');
hold on;
plot(x,y_exact,'b.-')
xlabel('X axis')
ylabel('Y axis')

legend('Y_e_x_a_c_t','Y_a_p_p')


%% defining the function according to the proplem
function dy = fn(~, y)
    dy = [0,  1
          2, -1] * y; %change the matrix due to your intital conditins 
                      %and the equation in your proplem
end


Unable to perform assignment because the size of the left side is 2-by-1 and the size of the right side is 2-by-2.

Error in HW3_multistep_method (line 30)
        yic(:,i+1) = yic(:, i) + h/6*(K11 + 2*K12 + 2*K21 + K22);
 
>> 

Answer 1

[Walter Roberson]

No, that error does not show up, but you had some other errors. I marked the changes with HERE

h=0.1;          %step size (changable according to the proplem)
x=0:h:1; %the X domain range
yic = [[1;-2],zeros(2, length(x)-1)]; %intial condition in form of matrix
                                      %(changable according to the proplem)
%*********************************************
%             Exact solution
%*********************************************
y_exact=exp(-2*x); %define your equation for exact solution
%**********************************************

%********* Numerical solution *****************
%% RK4th order definition 
for i = 1:3
        K11 = fn(x(i), yic(:, i));
        K12 = fn(x(i) + h/2, yic(:, i) + h*K11/2);
        K21 = fn(x(i) + h/2, yic(:, i) + h*K12/2);
        K22 = fn(x(i) + h,   yic(:, i) + h*K21);
        yic(:,i+1) = yic(:, i) + h/6*(K11 + 2*K12 + 2*K21 + K22);
end   
%%predictor corrector equation defenition
 for i = 5:11
        y_star=yic(:,i) + (h/24)*((55*fn(x(i),yic(:,i)))-(59*fn(x(i-1),yic(:,i-1))) +(37*fn(x(i-2),yic(:,i-2))) - (9*fn(x(i-3),yic(:,i-3))));
        yic(:,i+1) = yic(:,i)+(h/24)*((9*fn(x(i),y_star))+(19*fn(x(i),yic(:,i)))-(5*fn(x(i-1),yic(:,i-1)))+(fn(x(i-3),yic(:,i-3))));  %HERE
 end

%% print the output in the form of table
out=[x' y_exact' yic(1,1:end-1)'];         %HERE
fprintf(' ------------------------------------------------\n')

 ------------------------------------------------

fprintf('|   X    |  Y(exact)   |  Y(approximate))   |\n')

|   X    |  Y(exact)   |  Y(approximate))   |

fprintf(' ------------------------------------------------\n')

 ------------------------------------------------

fprintf('|  %3.1f   |  %3.6f   |     %3.6f       |\n',out')

|  0.0   |  1.000000   |     1.000000       |
|  0.1   |  0.818731   |     0.818733       |
|  0.2   |  0.670320   |     0.670324       |
|  0.3   |  0.548812   |     0.548817       |
|  0.4   |  0.449329   |     0.000000       |
|  0.5   |  0.367879   |     0.006703       |
|  0.6   |  0.301194   |     0.008704       |
|  0.7   |  0.246597   |     -0.000656       |
|  0.8   |  0.201897   |     -0.000329       |
|  0.9   |  0.165299   |     -0.000159       |
|  1.0   |  0.135335   |     -0.000266       |

fprintf(' ------------------------------------------------\n')

 ------------------------------------------------

%% plotting the grapgh
plot(x, yic(1,1:end-1), 'r*');   %HERE
hold on;
plot(x,y_exact,'b.-')
xlabel('X axis')
ylabel('Y axis')
legend('Y_a_p_p','Y_e_x_a_c_t')      %HERE

%% defining the function according to the proplem
function dy = fn(~, y)
    dy = [0,  1
          2, -1] * y; %change the matrix due to your intital conditins 
                      %and the equation in your proplem
end

[Mohammad Adeeb]

same error still appear

Unable to perform assignment because the size of the left side is 2-by-1 and the size of the right side is 2-by-2.

Error in HW3_multistep_method (line 30)

yic(:,i+1) = yic(:, i) + h/6*(K11 + 2*K12 + 2*K21 + K22);

[Walter Roberson]

I ran the code in R2020b (same version you indicate you are using) and my output is the same as what I posted above. The output I posted above has been run directly on R2021a on the Mathworks servers.

Your error is occuring on line 30 of your code according to the error message, but in the code you posted, that line is at most line 24, and is on line 18 of the code I posted. So you are not running the same code.

[Mohammad Adeeb]

No it’s the same , but i put it in a different m file and it’s worked , thanks alot