Three main contributions are presented in this paper. First, the septic quasi-interpolants are calculated with all their coefficients. Second, we explore the results to solve a generalized and broad class of Fredholm integral equations of the second kind. Finally, we present three degenerate kernel methods; the latter is a combination of the two previously established methods in the literature. Moreover, we provide a convergence analysis and we give new error bounds. Finally, we exhibit some numerical examples and compare them with previous results in the literature.

Three main contributions are presented in this paper. First, the septic quasi-interpolants are calculated with all their coefficients. Second, we explore the results to solve a generalized and broad class of Fredholm integral equations of the second kind. Finally, we present three degenerate kernel methods; the latter is a combination of the two previously established methods in the literature. Moreover, we provide a convergence analysis and we give new error bounds. Finally, we exhibit some numerical examples and compare them with previous results in the literature.

Many self-adaptation routing schemes have been proposed for sensor networks. The most relevant of them consider a hierarchical topology and aim to meet energy conservation and QoS requirements in a homogeneous environment. In such networks, one specific algorithm is commonly applied by all nodes inside clusters. Contrarily, in this paper, we propose a heterogeneous routing by applying different strategies according to specific parameters at the same time inside different clusters. Moreover, each cluster can adopt different strategies at different moments under different conditions. This approach leads to a new self-adaptation protocol based on heterogeneity of the routing process in a multi-hop clustering WSN. The proposal uses a set of mechanisms that have been adopted in well-known protocols (HEEP, APTEEN, LEACH, PEGASIS, etc.) taking into account their strengths and weaknesses. Simulations under NS2 show that our proposal, based on heterogeneous routing protocol, prolongs the network lifetime with different ratios compared to HEEP, PEGASIS and others.

Many self-adaptation routing schemes have been proposed for sensor networks. The most relevant of them consider a hierarchical topology and aim to meet energy conservation and QoS requirements in a homogeneous environment. In such networks, one specific algorithm is commonly applied by all nodes inside clusters. Contrarily, in this paper, we propose a heterogeneous routing by applying different strategies according to specific parameters at the same time inside different clusters. Moreover, each cluster can adopt different strategies at different moments under different conditions. This approach leads to a new self-adaptation protocol based on heterogeneity of the routing process in a multi-hop clustering WSN. The proposal uses a set of mechanisms that have been adopted in well-known protocols (HEEP, APTEEN, LEACH, PEGASIS, etc.) taking into account their strengths and weaknesses. Simulations under NS2 show that our proposal, based on heterogeneous routing protocol, prolongs the network lifetime with different ratios compared to HEEP, PEGASIS and others.