# BLUES iteration applied to nonlinear ordinary differential equations for wave propagation and heat transfer

@article{Berx2020BLUESIA, title={BLUES iteration applied to nonlinear ordinary differential equations for wave propagation and heat transfer}, author={Jonas Berx and Joseph O. Indekeu}, journal={Journal of Physics A: Mathematical and Theoretical}, year={2020}, volume={54} }

The iteration sequence based on the BLUES (Beyond Linear Use of Equation Superposition) function method for calculating analytic approximants to solutions of nonlinear ordinary differential equations with sources is elaborated upon. Diverse problems in physics are studied and approximate analytic solutions are found. We first treat a damped driven nonlinear oscillator and show that the method can correctly reproduce oscillatory behavior. Next, a fractional differential equation describing heat…

## 6 Citations

### BLUES function method applied to partial differential equations and analytic approximants for interface growth under shear

- PhysicsPhysical Review Research
- 2021

Abstract An iteration sequence based on the BLUES (Beyond Linear Use of Equation Superposition) function method is presented for calculating analytic approximants to solutions of nonlinear partial…

### Analytic approximants for Aeolian dunes from the BLUES function method applied to partial differential equations

- Physics
- 2021

Abstract An iteration sequence based on the BLUES (Beyond Linear Use of Equation Superposition) function method is presented for calculating analytic approximants to solutions of nonlinear partial…

### The BLUES function method for second-order partial differential equations: application to a nonlinear telegrapher equation

- MathematicsPartial Differential Equations in Applied Mathematics
- 2022

### Epidemic processes with vaccination and immunity loss studied with the BLUES function method

- MathematicsPhysica A: Statistical Mechanics and its Applications
- 2021

### Convergence acceleration for the BLUES function method

- MathematicsArXiv
- 2022

A detailed comparison is made between four di ﬀ erent iterative procedures: Picard, Ishikawa, Mann and Picard-Krasnoselskii, within the framework of the BLUES function method and the variational…

### Analytic approximants for interface growth under shear from the BLUES function method applied to partial differential equations

- Physics
- 2021

Abstract An iteration sequence based on the BLUES (Beyond Linear Use of Equation Superposition) function method is presented for calculating analytic approximants to solutions of nonlinear partial…

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