用matlab编程隐式示欧拉法解决如下问题dudt = −4u + 6v u0 = 1dvdt = 3u − 7v v0 = 20t1

step = 0.01; % 步长 t = 0:step:1; % 时间范围 u = zeros(size(t)); % 初始化u v = zeros(size(t)); % 初始化v u(1) = 1; % 初始值 v(1) = 2; % 初始值 for i = 2:length(t) % 对u的隐式欧拉法 u(i) = (u(i-1) + step*(6v(i-1))) / (1 + 4step); % 对v的隐式欧拉法 v(i) = (v(i-1) + step*(3u(i) - 7v(i-1))) / (1 + 7*step); end plot(t, u, t, v); legend('u', 'v'); xlabel('t'); ylabel('u/v');