Improved numerical solutions for chaotic-cancer-model
Source abstract
Abstract
In biological sciences, dynamical system of cancer model is well known due to its sensitivity and chaoticity. Present work provides detailed computational study of cancer model by counterbalancing its sensitive dependency on initial conditions and parameter values. Cancer chaotic model is discretized into a system of nonlinear equations that are solved using the well-known Successive-Over-Relaxation (SOR) method with a proven convergence. This technique enables to solve large systems and provides more accurate approximation which is illustrated through tables, time history maps and phase portraits with detailed analysis.
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Research context
OpenAlex topics: Mathematical Biology Tumor Growth · Model Reduction and Neural Networks · Gene Regulatory Network Analysis
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
Affiliations
Institute of Space Technology 1 Department of Applied Mathematics and Statistics, , Islamabad 44000, Pakistan
Air University 2 Department of Computer Science, , Multan Campus, Islamabad 44000, Pakistan
Funding
Higher Education Commission, Pakistan
References (19)
Show source-provided references
1. Mathematical model of cancer treatments using immunotherapy, chemotherapy and biochemotherapy10.12988/ams.2013.13023 ↗
2. A mathematical model of Gene therapy for the treatment of cancer
3. Mathematical modeling of strategic treatments on tumor growth10.4172/2168-9679.1000140 ↗
4. Control of nonlinear dynamics: Where do models fit in10.1142/s0218127400000475 ↗
5. On nonlinear control design for autonomous chaotic systems of integer and fractional orders10.1016/s0960-0779(02)00644-6 ↗
6. Synchronization in chaotic system10.1103/PhysRevLett.64.821 ↗
7. On immunotherapies and cancer vaccination protocols: A mathematical modeling approach10.1016/j.jtbi.2009.05.001 ↗
8. Chaos in a three-dimensional cancer model10.1142/S0218127410025417 ↗
9. An analysis of the properties of the variants of Newton’s method with third order convergence10.1016/j.amc.2006.05.116 ↗
10. Variants of Newton’s method for functions of several variables10.1016/j.amc.2006.05.062 ↗
11. A uniparametric Halley-type iteration with free second derivative10.1016/j.cam.2004.02.020 ↗
12. On Halley-type iterations with free second derivative10.1016/j.cam.2004.02.020 ↗
13. Improvements of the efficiency of some three-step iterative Newton-like methods10.1007/s00211-007-0088-8 ↗
14. Second-derivative-free variant of the Chebyshev method for nonlinear equations10.1023/a:1004618223538 ↗
15. Modified Newton method with cubic convergence: The multivariate case10.1016/j.cam.2003.12.041 ↗
16. Accelerated methods of order 2p for systems of nonlinear equations10.1016/j.cam.2009.11.018 ↗
17. Efficient high-order methods based on golden ratio for nonlinear systems10.1016/j.amc.2010.11.006 ↗
18. Third-order methods from quadrature formulae for solving systems of nonlinear equations10.1016/s0096-3003(03)00178-4 ↗
19. Norollah Darvishi, SOR- Steffensen-Newton method to solve systems of nonlinear equations10.5923/j.am.20120202.05 ↗