论文标题
CK真实功能和应用程序中的添加定理在普通微分方程中
Addition theorems for Ck real functions and applications in ordinary differential equations
论文作者
论文摘要
这项工作确定了CK真实标量函数的添加定理和双角度公式的存在。此外，我们确定双变量函数的必要条件是CK真实函数的添加公式。双角度公式允许我们生成复制算法，该算法可用作经典数值方法的替代方法，以获得用于解决普通微分方程解决方案的近似值。我们证明，该算法在该溶液的最大结构域中包含的任何紧凑型结构域中均匀收敛。最后，我们进行一些数值模拟，显示与标准数值方法相比，重复算法的性能良好
This work establishes the existence of addition theorems and double-angle formulas for Ck real scalar functions. Moreover, we determine necessary and sufficient conditions for a bivariate function to be an addition formula for a Ck real function. The double-angle formulas allow us to generate a duplication algorithm, which can be used as an alternative to the classical numerical methods to obtain an approximation for the solution of an ordinary differential equation. We demonstrate that this algorithm converges uniformly in any compact domain contained in the maximal domain of that solution. Finally, we carry out some numerical simulations showing a good performance of the duplication algorithm when compared with standard numerical methods
