Improved accuracy and convergence of homotopy‐based solutions for aggregation–fragmentation models
Prakrati Kushwah, Jitraj Saha
Abstract
We discuss the formulation of a numerical scheme based on the homotopy method to solve different aggregation–fragmentation models including the simultaneous event. Several test cases are considered and analyzed qualitatively and quantitatively to ascertain the improved accuracy and efficiency of the proposed model over the existing semi‐analytical models. The generalized solution of the truncated problem is obtained for some test cases, which in the limiting sense tends to the exact solution. A detailed convergence analysis of the scheme is also studied.
Topics & Concepts
MathematicsHomotopy analysis methodConvergence (economics)Applied mathematicsLimitingHomotopyFragmentation (computing)Scheme (mathematics)Mathematical optimizationExact solutions in general relativityMathematical analysisComputer sciencePure mathematicsEconomic growthEconomicsEngineeringMechanical engineeringOperating systemCoagulation and Flocculation StudiesFractional Differential Equations SolutionsField-Flow Fractionation Techniques