Finite difference schemes for time-dependent convection q-diffusion problem

Finite difference schemes for time-dependent convection q-diffusion problem

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The energy balance ordinary differential equations (ODEs) model of climate change is extended to whirlwind direct2 the partial differential equations (PDEs) model with convections and q-diffusions.Instead of integer order second-order partial derivatives, partial q-derivatives are considered.The local stability analysis of the ODEs model is established using the Routh-Hurwitz criterion.A numerical scheme is constructed, which is explicit and second-order in time.For spatial derivatives, second-order central difference formulas are employed.

The stability condition of the numerical scheme for the system of convection q-diffusion equations is found.Both types of ODEs and PDEs models are solved with the constructed scheme.A comparison of the constructed scheme with the existing first-order scheme rt100 mini bike parts is also made.The graphical results show that global mean surface and ocean temperatures escalate by varying the heat source parameter.Additionally, these newly established techniques demonstrate predictability.