Obeidat Nazek A, Rawashdeh Mahmoud Saleh, Al Smadi Mohammad N
Department of Mathematics and Statistics, Jordan University of Science and Technology, Irbid, Jordan.
Sci Prog. 2024 Apr-Jun;107(2):368504241256864. doi: 10.1177/00368504241256864.
One of the most noteworthy differential equations of the first order is the Riccati differential equation. It is applied in various branches of mathematics, including algebraic geometry, physics, and conformal mapping theory. The -transform Adomian decomposition method is employed in the current study to find exact solutions for different kinds of nonlinear differential equations. We give thorough detailed proofs for new theorems related to the -transform technique. The Adomian decomposition method and the -transform method serve as the foundation for this technique. For certain differential equations, the theoretical analysis of the -transform Adomian decomposition method is examined and is computed using readily computed terms. Our findings are contrasted with exact solutions found in the literature that were produced using alternative techniques. The significant features of the -transform Adomian decomposition method are described in the article. It has been shown that the -transform Adomian decomposition method is very efficient, useful, and adaptable to a broad variety of linear and nonlinear differential equations. Most of the symbolic and numerical calculations were performed using Mathematica.
一阶最值得注意的微分方程之一是里卡蒂微分方程。它应用于数学的各个分支，包括代数几何、物理学和共形映射理论。当前研究采用 - 变换阿多米安分解法来求解不同类型的非线性微分方程。我们为与 - 变换技术相关的新定理给出了详尽的证明。阿多米安分解法和 - 变换法是该技术的基础。对于某些微分方程，研究了 - 变换阿多米安分解法的理论分析，并使用易于计算的项进行计算。我们的结果与文献中使用其他技术得到的精确解进行了对比。文章描述了 - 变换阿多米安分解法的显著特征。结果表明， - 变换阿多米安分解法非常有效、有用，并且适用于各种各样的线性和非线性微分方程。大多数符号和数值计算是使用Mathematica进行的。
