Numerical scheme and analytical solutions to the stochastic nonlinear advection diffusion dynamical model

Muhammad Waqas Yasin, Muhammad Sajid Iqbal, Aly R. Seadawy, Muhammad Zafarullah Baber, Muhammad Younis, Syed T. R. Rizvi

2021International Journal of Nonlinear Sciences and Numerical Simulation36 citationsDOI

Abstract

Abstract In this study, we give the numerical scheme to the stochastic nonlinear advection diffusion equation. This models is considered with white noise (or random process) having same intensity by changing frequencies. Furthermore, the stability and consistency of proposed scheme are also discussed. Moreover, it is concerned about the analytical solutions, the Riccati equation mapping method is adopted. The different families of single (shock and singular) and mixed (complex solitary-shock, shock-singular, and double-singular) form solutions are obtained with the different choices of free parameters. The graphical behavior of solutions is also depicted in 3D and corresponding contours.

Topics & Concepts

Shock (circulatory)Nonlinear systemAdvectionMathematicsConsistency (knowledge bases)Applied mathematicsStability (learning theory)White noiseDiffusionRiccati equationDiffusion processMathematical analysisStatistical physicsPhysicsComputer scienceGeometryPartial differential equationInternal medicineQuantum mechanicsStatisticsMedicineKnowledge managementInnovation diffusionThermodynamicsMachine learningFluid Dynamics and Turbulent FlowsDifferential Equations and Numerical MethodsFractional Differential Equations Solutions