We introduce TiNy Titans (TNT), the first systematic study of star formation and the subsequent processing of the interstellar medium in interacting dwarf galaxies. Here we present the first results from a multiwavelength observational program based on a sample of 104 dwarf galaxy pairs selected from a range of environments within the spectroscopic portion of the Sloan Digital Sky Survey and caught in various stages of interaction. The TNT dwarf pairs span mass ratios of M * ,1 /M * ,2 < 10, projected separations < 50 kpc, and pair member masses of 7 < log(M * /M ⊙ ) < 9.7. The dwarf-dwarf merger sequence, as defined by TNT at z=0, demonstrates conclusively and for the first time that the star formation enhancement observed for massive galaxy pairs also extends to the dwarf mass range. Star formation is enhanced in paired dwarfs in otherwise isolated environments by factor of 2.3 (± 0.7) at pair separations < 50 kpc relative to unpaired analogs. The enhancement decreases with increasing pair separation and extends out to pair separations as large as 100 kpc. Starbursts, defined by Hα EQW > 100Å, occur in 20% of the TNT dwarf pairs, regardless of environment, compared to only 6-8% of the matched unpaired dwarfs. Starbursts can be triggered throughout the merger (i.e. out to large pair separations) and not just approaching coalescence. Despite their enhanced star formation and triggered starbursts, most TNT dwarf pairs have similar gas fractions relative to unpaired dwarfs of the same stellar mass. Thus, there may be significant reservoirs of diffuse, nonstarforming neutral gas surrounding the dwarf pairs or the gas consumption timescales may be long in the starburst phase. The only TNT dwarf pairs with low gas fractions (f gas < 0.4) and the only dwarfs, either paired or unpaired, with Hα EQW < 2Å are found near massive galaxy hosts. We conclude that dwarf-dwarf interactions are significant drivers of galaxy evolution at the low mass end, but ultimately environment is responsible for the quenching of star formation. This preliminary study is a precursor to an ongoing high resolution H i and optical imaging program to constrain the spatial distribution of star formation and gas throughout the course of the dwarf-dwarf merger sequence.

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In this paper, the sinc-derivative collocation approach is used to solve second order integro-differential boundary value problems. While the derivative of the unknown variables is interpolated using sinc numerical methods, the desired solution and the integral terms are evaluated through numerical integration and all higher order derivatives are approximated through successive numerical differentiation. Suitable transformations are used to reduce non-homogeneous boundary conditions to homogeneous. Comparison of the proposed method with different approaches that were previously considered in the literature is carried out in order to test its accuracy and efficiency. The results show that the sinc-derivative collocation method performs well.