The semi-analytical method obtains the solution for linear/nonlinear ODEs and PDEs in series form. This article presents a novel semi-analytical approach named Daftardar-Jafari method (DJM) to solve integro-partial differential equation such as breakage and nonlinear aggregation-breakage equations (ABE). Four test cases for the breakage equation are used to acquire closed form series solutions. Further, numerical findings such as number density and moments are compared with the analytical solutions to show the efficiency and accuracy of the method. Moreover, the DJM is employed to solve the well-known ABE, and truncated solutions are presented for the two test cases. In addition, absolute errors over various time periods are depicted in the form of tables.
翻译：半解析方法是一种获取线性/非线性常微分方程和偏微分方程解的级数展开方法。本文提出了一种名为狄夫达尔－贾法里方法的半解析方法，用于求解破碎和非线性聚合破碎方程（ABE等）。通过破碎方程的四个测试案例，得出闭合形式级数解。而且，为了展示该方法的效率和准确性，还将数值结果（例如数密度和矩）与分析解进行了比较。此外，狄夫达尔－贾法里方法也被用于求解著名的ABE，为两个测试案例展示了截断解。此外，还将各个时段的绝对误差制成表格形式。
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