The Influence of the Perturbation of the Initial Data on the Analytic Approximate Solution of the Van der Pol Equation in the Complex Domain
В. Н. Орлов, Alexander Chichurin
Abstract
In this paper, we substantiate the analytical approximate method for Cauchy problem of the Van der Pol equation in the complex domain. These approximate solutions allow analytical continuation for both real and complex cases. We follow the influence of variation in the initial data of the problem in order to control the computational process and improve the accuracy of the final results. Several simple applications of the method are given. A numerical study confirms the consistency of the developed method.
Topics & Concepts
Van der Pol oscillatorContinuationApplied mathematicsConsistency (knowledge bases)Domain (mathematical analysis)Cauchy distributionAnalytic continuationPerturbation (astronomy)MathematicsComputer scienceMathematical analysisPhysicsGeometryProgramming languageQuantum mechanicsNonlinear systemDifferential Equations and Numerical MethodsNumerical methods for differential equationsFractional Differential Equations Solutions