Matlab Picard方法-将现有的符号赋给向量

Question

我正在为matlab中的picard方法编写一个程序。这需要对要被积分多项式替换的函数进行多次迭代。

现在我有一个已有的带有syms x的多项式，它由一个向量a定义：

 for i = 1:degree+1
     polynomial = symfun(polynomial + a(i) *x^(i-1), x);
 end

 syms t;
 y = symfun( zeros(1,maxIterations+1),x);
 y(1) = polynomial;

 for i = 2: maxIterations
   substitute = subs(polynomial, x, y(i-1));
   y(i) = symfun(x0 + int( substitute, t), x);  %for some predefined x0
 end

但是当我尝试使用y(1) = symfun(polynomial,x);时，它失败了，给出了一个错误：

无效的索引或函数定义。在定义函数时，请确保参数是符号变量，函数的主体是SYM表达式。索引时，输入必须是数字、逻辑或“：”。

但是，既然polynomial只是一个辛函数，为什么不能将它分配给向量y中的一个槽呢？在定义时，我已经尝试过使用feval()，而不是使用symfun()，但是到目前为止没有什么效果。

完整代码：

    %%Input

prompt = 'What is the degree of the polynomial?   \n ';
degree = input(prompt);

a = zeros(degree+1,1);
for i = 1:degree+1
    a(i) = input(['Enter value of coefficient a_' num2str(i-1) ': ']);
end

prompt = 'What is the number of iterations?   \n ';
maxIterations = input(prompt);

prompt = 'What is the value of x0?   \n ';
x0 = input(prompt);

%%Computing Integrated Vector

aInt = [0];
for i = 1:degree+1
    aInt(i+1) = a(i)/(i);
end

fprintf('x0');
for i = 1: degree+1
  fprintf( [' + ' num2str(aInt(i+1)) ' x^' num2str(i)] );
end

fprintf('\n');

syms x;
polynomial = 0;

for i = 1: degree+1

    polynomial = symfun(polynomial + a(i) * x ^(i-1), x);  

end

%Picard Method
syms t;
syms y;
y = symfun( zeros(maxIterations+1,1), x );
y(1) = polynomial;
for i = 2: maxIterations
    substitute = subs(polynomial, x, y(i-1));
    y(i) = symfun(x0 + int( substitute,t ), t);

end

for i = 1:maxIterations
    fprintf(['x_' num2str(i-1) ' = ' y(i), ' \n']);
end

提前感谢！

Answer 1

修好了！这是工作密码。(其中可能仍有轻蔑的错误)。这个错误没有正确地定义polynomial，因为我首先使用了syms(polynomial)，它导致多项式的和将‘多项式’作为一个变量。考虑picard方法，还修正了一些轻微的错误，如y(1)的定义。

%%Input

prompt = 'What is the degree of the polynomial?   \n ';
degree = input(prompt);

a = zeros(degree+1,1);
for i = 1:degree+1
    a(i) = input(['Enter value of coefficient a_' num2str(i-1) ': ']);
end

prompt = 'What is the number of iterations?   \n ';
maxIterations = input(prompt);

prompt = 'What is the value of x0?   \n ';
x0 = input(prompt);

%%Computing Integrated Vector

aInt = [0];
for i = 1:degree+1
    aInt(i+1) = a(i)/(i);
end

%%vector print

fprintf('x0');
for i = 1: degree+1
  fprintf( [' + ' num2str(aInt(i+1)) ' x^' num2str(i)] );
end

fprintf('\n');

syms x;
polynomial = 0; 

for i = 1: degree+1

    polynomial = polynomial + symfun(a(i) * x ^(i-1), x);  

end

%Picard Method
syms t;
syms y;
y = sym( 'y', [1 maxIterations] );
y(1) = x0;

for i = 2: maxIterations
    substitute = subs(polynomial, x, y(i-1));
    y(i) = symfun(x0 + int( substitute, t ), t);
end

for i = 1:maxIterations
    fprintf('The iteration y_%d = %s \n',(i-1), y(i))

end

%plot graphs