基于Matlab-GUI的数值积分界面设计

The Numerical Integration Design Based on Matlab-GUI

为了解决原函数完全未知、原函数已知但其形式复杂、原函数已知且存在解析解3种情况下的复杂积分计算问题,提出了关于数值积分界面的设计。将Matiab中可开发的GUI工具结合数值积分计算中的典型算法构造开放式的用户界面,设计出数值积分求解器并实现数值积分可视化功能;同时通过采用自定义方式设置积分区间等分数的思路,提高了梯形、辛普森、复合梯形、高斯-勒让德数和自适应5种积分方法的计算精度。最后,用所设计的数值积分GUI界面对3种类型复杂积分函数进行验证和求解,结果表明,该设计能在同一界面同时实现用5种积分方法按用户任意设定的精度进行积分求解并能将计算结果可视化,因此该界面具有适应性强、使用方便、界面友好、操作简洁的优点。

This paper puts forward the problem about the design of numerical integral interface,to solve the complex integral calculation under three situations：first,the function is completely unknown;second,the function is known while its form is complex;third,the function is known and the analytical solutions exist.Combining the GUI tool which can be developed in Matlab with typical algorithm in the calculation of numerical integration,this paper constructs an open users＇ interface,and designs the numerical integral solver even realize visualization of the numerical integration.At the same time,the thinking of using a custom way to set integral interval equivalent fractions has improved the computational accuracy of five integral methods.Finally,the designed numerical integration GUI interface is used to verify three types of complex integral function.The results show that the design can solve the integration at any set accuracy by using the five methods in the same interface,and visualizes the computed results.Therefore,the designed interface has advantages of strong adaptability,convenience,friendliness and simple operation.