function data = Adams_PECE(x0,y0,h,N)
global diff_f;
%函數功能：四階Adams預測－校正方法.
%輸入參數：（x0，y0）－－初值；h－－步長；N－－計算次數.
%返 回 值：解曲線上的點，格式為二維列向量，第一列為自變量，第二列為函數值.
%調用關系：調用四階龍格－庫塔法函數Adams_RK_four_step(x0,y0,h,N)產生初值.

syms x y;
diff_f = input('請輸入微分函數dy/dx:');

data(1,1) = x0;
data(1,2) = y0;

%四階龍格－庫塔法提供初值.
data_RK = Adams_RK_four_step(x0,y0,h,3);
data(2,:) = data_RK(2,:);
data(3,:) = data_RK(3,:);
data(4,:) = data_RK(4,:);
x_former = data(4,1);
y_former = data(4,2);
for i = 1:4
    x = data(i,1);
    y = data(i,2);
    dy(i) = eval(diff_f);
end

for i = 4:N
    x = x_former + h;
    y = y_former + h * (55 * dy(i) - 59 * dy(i-1) + 37 * dy(i-2) - 9 * dy(i-3)) / 24;
    dy_p = eval(diff_f);
    y = y_former + h * (9 * dy_p + 19 * dy(i) - 5 * dy(i-1) + dy(i-2)) / 24;
    dy(i+1) = eval(diff_f);
 
    %保存數據.   
    data(i+1,1) = x;
    data(i+1,2) = y;
    
    %更新數據.
    x_former = x;
    y_former = y;
end