This paper presents seven modified Adomian Decomposition Method (ADM) techniques for efficiently solving initial value problems, especially those involving non-homogeneous and nonlinear differential equations. While the classical ADM is effective for linear homogeneous cases, it has difficulties solving more complex problems. The proposed modifications—from MADM1 to MLADM—include Maclaurin and Taylor expansions, Laplace transforms, and single-step iterations.• These modifications enhance convergence, reduce complexity, and improve accuracy.• Each method offers specific advantages, such as accelerating convergence (MADM2, RADM4), simplifying computation (TSADM5), and achieving higher accuracy (MLADM).• Numerical examples confirm the accuracy and efficiency of all methods, highlighting their superiority over the classical ADM.
The present study introduces description of a new species of genus Arboridia Zakhvaticin 1946, based on a large collection of Cicadellids. External morphological characters particularly male genitalia were discussed and illustrated. The genus Arboridia Zalchvatkiia (Typhlocybinae: Erythroneurini) contains small slender, fragil and attractively coloured and patterned leafhoppers. It was erected by Zakhvatkin in 1946 (Zalchvatkin, 1946). The overall length of adults ranges from 2.5 to 3.4 mm. Members of this genus can be recognized by inner apical cell of forewing which is long with oblique base; Cu confluent with this base at a point near the middle of the length of inner apical cell; two prominent circular deep brown spots on vertex (Zal
... Show MoreNew Fourteen compounds were synthesized in four steps. The first step included synthesis of 2-biphenyl fused ring of imidazo(1,2- a)pyrimidine from the reaction of 2-aminopyrimidine and biphenyl phenacyl bromide . The second step was introduced aldehyde group from the reaction of 2-biphenyl fused rings of imidazo(1,2-a)pyrimidine with POCl3 in presence of DMF and CHCl3. 3-Carbaladehyde derivatives of fused imidazo/pyrimidine was reacted with different aromatic amines to afford new Schiff bases. These new 3- imines derivatives was reduced by using sodiumborohydride to yield another new 3-aminomethyl-2-biphenyl imidazo (1,2-a)pyrimidine derivatives in moderate yield .Some new prepared compounds were identified by melting point, FT- IR , 13C-
... Show MoreIn this study, synthesised new ligand: potassium 2,2'-(quinoxaline-2,3- diyl)bis(1-phenylhydrazinecarbodithioate) (L). The ligand synthesised by reacting N1,N2-dip-tolyloxalamide as the starting material with CS2 and KOH to add the CS2 group and then with phenylendiammine to achieve (L). The ligand used in the synthesis of complexes with (CoII, NiII and CdII). The new ligand and its complexes characterised by FT-IR, UV-Vis, 1H, 13C-NMR, Mass spectroscopy, and elemental analysis, in addition to the above techniques were using magnetic moment, atomic absorption, chloride content, and melting point to describe the metal complexes.
A new series of transition metal complexes of Cu(II), Ni(II), Co(II) and Fe(III) have been synthesized from the Schiff base (L1) and (L2) derived from Semicarbazide hydro chloride and 4-chlorobenzaldehyde or 4-bromobenzaldehyde. The structural features have been arrived from their elemental analyses, magnetic susceptibility, molar conductivity, IR, UV-Vis. and 1H NMR spectral studies. The data show that the complexes have composition of [M(L)2](NO3)2 and [Fe(L)2 (NO3)2](NO3) where the M=Co(II),Ni(II) and Cu(II) ;L=L1and L2 type. The magnetic susceptibility and UV-Vis spectral data of the complexes suggest a square planer geometry for Co(II) and Cu(II) but Fe(III) octahedral geometry and Ni(II) tetrahedral geometry around the central metal i
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... Show MoreObjective: Schiff’s and Mannich bases of isatins are an important group of heterocyclic compounds which are of great importance in medicinal chemistry as antimicrobial agents. In the vision of these facts, new bis-Schiff bases and Mannich bases of isatins were synthesized. Methods: Three different bis-Schiff bases (3a-c) have been synthesized by reacting isatin, 5-fluoroisatin and 5-methoxy isatin with thiophene-2- carboxaldehyde using hydrazine hydrate to link between the carbonyl compounds, and then these bis- Schiff bases were condensed with two different secondary amines (piperidine and morpholine) separately, and formaldehyde to form the Mannich bases (4a-c and 5a-f), respectively. Results: The structures of the newly synthesized com
... Show MoreThis research includes synthesis of new heterocyclic derivatives of N-benzyl-5-bromoisatin. New 1, 2, 4-triazole, oxazoline and thiazoline derivatives of [N-benzyl-5-bromo-3-(Ethyliminoacetate)-indole-2-one] (2) have been synthesized. The preparation process started by the reaction of 5-bromoisatin with sodium hydride in dimethylformamide (DMF) at 0°C, gave suspension of sodium salt of 5-bromoisatin and subsequent reaction with benzylchloride to give N-benzyl-5-bromoisatin (1). Compound (1) reacted with ethylglycinate (Schiff base) obtained the intermediate compound (2) which reacted with different reagents in two ways. The first way, compound (2) reacted with (hydrazine hydrate, semicarbazide, phenylsemicarbazide and thiosemicarbazide)
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