微分方程(ODEs)解算器(中文版).docx

微分方程(ODEs)解算器1.先来认识下常微分方程(ODE)初值问题解算器(solver)[T,Y,TE,YE,IE] = odesolver(odefun,tspan,y0,options)sxint = deval(sol,xint)Matlab中提供了以下解算器：输入参数：odefun：微分方程的Matlab语言描述函数，必须是函数句柄或者字符串，必须写成Matlab规范格式(也就是一阶显式微分方程组)tspan=[t0 tf]或者[t0,t1,…tf]：微分变量的范围，两者都是根据t0和tf的值自动选择步长，只是前者返回所有计算点的微分值，而后者只返回指定的点的微分值，一定要注意对于后者tspan必须严格单调，还有就是两者数据存储时使用的内存不同(明显前者多)，其它没有任何本质的区别y0=[y(0),y’(0),y’’(0)…]：微分方程初值，依次输入所有状态变量的初值options：微分优化参数，是一个结构体，使用odeset可以设置具体参数，详细内容查看帮助(如下是Matlab 中odeset的说明： help odeset ODESET Create/alter ODE OPTIONS structure. OPTIONS = ODESET(NAME1,VALUE1,NAME2,VALUE2,...) creates an integrator options structure OPTIONS in which the named properties have the specified values. Any unspecified properties have default values. It is sufficient to type only the leading characters that uniquely identify the property. Case is ignored for property names. OPTIONS = ODESET(OLDOPTS,NAME1,VALUE1,...) alters an existing options structure OLDOPTS. OPTIONS = ODESET(OLDOPTS,NEWOPTS) combines an existing options structure OLDOPTS with a new options structure NEWOPTS. Any new properties overwrite corresponding old properties. ODESET with no input arguments displays all property names and their possible values. ODESET PROPERTIES RelTol - Relative error tolerance [ positive scalar {1e-3} ] This scalar applies to all components of the solution vector, and defaults to 1e-3 (0.1% accuracy) in all solvers. The estimated error in each integration step satisfies e(i) = max(RelTol*abs(y(i)),AbsTol(i)). AbsTol - Absolute error tolerance [ positive scalar or vector {1e-6} ] A scalar tolerance applies to all components of the solution vector. Elements of a vector of tolerances apply to corresponding components of the solution vector. AbsTol defaults to 1e-6 in all solvers. See RelTol. NormControl - Control error relative to norm of solution [ on | {off} ] Set this property on to request that the solvers control the error in each integration step with norm(e) = max(RelTol*norm(y),AbsTol). By de