how can i solve this error , predictor corrector method

Question

Mohammad Adeeb 2021-3-28

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/785846-how-can-i-solve-this-error-predictor-corrector-method

评论： Mohammad Adeeb 2021-3-28

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);
 
>> 

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Answer 1

Walter Roberson 2021-3-28

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/785846-how-can-i-solve-this-error-predictor-corrector-method#answer_660751

在 MATLAB Online 中打开

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

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Walter Roberson 2021-3-28

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 2021-3-28