clear all; clc; close all; clf;
sinan = sinan();
t0 = 0; tfinal = 60; N = 100;
h = (tfinal-t0)/N;
t = t0:h:tfinal;
%% Initial conditions
y0=[100, 10, 20];
y01=[100];
%% Parameters
Lambda = 0.1; beta = 0.4; mu = 0.01; gamma = 0.7; % parameters for model 1
a = 0.2; % parameter for model 2
Models
SIR Epidemic model
subject to
Decay model
subject to 
%% Models
model_1 = @(t, X) [Lambda- beta*X(1)*X(2);
beta*X(1)*X(2)-(gamma+mu)*X(2);
mu*X(2)];
model_2 = @(t, y) -a*y;
% fractional order
alpha = 1;
% Choose a solver
solver_1 = 'caputo';
solver_2 = 'abc';
solver_3 = 'CLASSICAL';
% How to solve a system of equations?
[t_euler_caputo_1, y_euler_caputo_1] = sinan.euler(model_1, alpha, t, h, y0, solver_1);
[t_euler_ABC_1, y_euler_ABC_1] = sinan.euler(model_1, alpha, t, h, y0, solver_2);
[t_euler_clas_1, y_euler_clas_1] = sinan.euler(model_1, alpha, t, h, y0, solver_3);
[t_rk4_caputo_1, y_rk4_caputo_1] = sinan.rk4(model_1, alpha, t, h, y0, solver_1);
[t_rk4_ABC_1, y_rk4_ABC_1] = sinan.rk4(model_1, alpha, t, h, y0, solver_2);
[t_rk4_clas_1, y_rk4_clas_1] = sinan.rk4(model_1, alpha, t, h, y0, solver_3);
% How to solve an equation?
[t_euler_caputo_2, y_euler_caputo_2] = sinan.euler(model_2, alpha, t, h, y01, solver_1);
[t_euler_ABC_2, y_euler_ABC_2] = sinan.euler(model_2, alpha, t, h, y01, solver_2);
[t_euler_clas_2, y_euler_clas_2] = sinan.euler(model_2, alpha, t, h, y01, solver_3);
[t_rk4_caputo_2, y_rk4_caputo_2] = sinan.rk4(model_2, alpha, t, h, y01, solver_1);
[t_rk4_ABC_2, y_rk4_ABC_2] = sinan.rk4(model_2, alpha, t, h, y01, solver_2);
[t_rk4_clas_2, y_rk4_clas_2] = sinan.rk4(model_2, alpha, t, h, y01, solver_3);
figure(1)
plot(t_euler_caputo_1, y_euler_caputo_1(:, 1), 'r', t_euler_ABC_1, y_euler_ABC_1(:, 1), 'b', t_euler_clas_1, y_euler_clas_1(:, 1), 'k')
legend('Euler caputo', 'Euler abc', 'Euler classical')
figure(2)
plot(t_rk4_caputo_1, y_rk4_caputo_1, 'r', t_rk4_ABC_1, y_rk4_ABC_1, 'b', t_rk4_clas_1, y_rk4_clas_1, 'k')
legend('rk4 caputo', 'rk4 abc', 'rk4 classical')
figure(3)
plot(t_euler_clas_1, y_euler_clas_1, 'r', t_rk4_clas_1, y_rk4_clas_1, 'b')
legend('euler classical', 'rk4 classical')
figure(4)
plot(t_euler_caputo_2, y_euler_caputo_2, 'r', t_euler_ABC_2, y_euler_ABC_2, 'b', t_euler_clas_2, y_euler_clas_2, 'k')
legend('Euler caputo', 'Euler abc', 'Euler classical')
xlabel('time (t)')
ylabel('y(t)')
figure(5)
plot(t_rk4_caputo_2, y_rk4_caputo_2, 'r', t_rk4_ABC_2, y_rk4_ABC_2, 'b', t_rk4_clas_2, y_rk4_clas_2, 'k')
legend('rk4 caputo', 'rk4 abc', 'rk4 classical')
xlabel('time (t)')
ylabel('y(t)')
figure(6)
plot(t_euler_clas_2, y_euler_clas_2, 'r', t_rk4_clas_2, y_rk4_clas_2, 'b')
legend('euler classical', 'rk4 classical')
xlabel('time (t)')
ylabel('y(t)')
引用格式
Muhammad Sinan (2026). sinan (https://ww2.mathworks.cn/matlabcentral/fileexchange/132812-sinan), MATLAB Central File Exchange. 检索时间: .
Sinan, Muhammad. Sinan. Zenodo, 2023, doi:10.5281/ZENODO.8189815.
致谢
参考作品: Digital Fractional Order Differentiator/integrator - IIR type, 微分方程式論(Introduction of Differential Equations), Non-linear equations system solver (Newton Raphson), Tutorial on solving DDEs with DDE23, Fractional Differential Equation Exact Solution, Tutorial on solving BVPs with BVP4C, Ordinary Differential Equation Toolbox: ODEbox Version 1.1, Qualitative Analysis of ODEs
